%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG156+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.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 18:30:40 EDT 2022 % Result : Unsatisfiable 10.13s 10.30s % Output : Proof 10.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : ALG156+1 : TPTP v8.1.0. Released v2.7.0. % 0.06/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n025.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 : Thu Jun 9 00:42:35 EDT 2022 % 0.12/0.34 % CPUTime : % 10.13/10.30 (* PROOF-FOUND *) % 10.13/10.30 % SZS status Unsatisfiable % 10.13/10.30 (* BEGIN-PROOF *) % 10.13/10.30 % SZS output start Proof % 10.13/10.30 Theorem zenon_thm : False. % 10.13/10.30 Proof. % 10.13/10.30 assert (zenon_L1_ : (((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H1d. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H21. zenon_intro zenon_H20. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H1f. zenon_intro zenon_H21. % 10.13/10.30 exact (zenon_H21 zenon_H1f). % 10.13/10.30 (* end of lemma zenon_L1_ *) % 10.13/10.30 assert (zenon_L2_ : (((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H22. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H1f. zenon_intro zenon_H23. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H23). zenon_intro zenon_H21. zenon_intro zenon_H24. % 10.13/10.30 exact (zenon_H21 zenon_H1f). % 10.13/10.30 (* end of lemma zenon_L2_ *) % 10.13/10.30 assert (zenon_L3_ : (((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H25. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H1f. zenon_intro zenon_H26. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H21. zenon_intro zenon_H27. % 10.13/10.30 exact (zenon_H21 zenon_H1f). % 10.13/10.30 (* end of lemma zenon_L3_ *) % 10.13/10.30 assert (zenon_L4_ : (((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H28. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H1f. zenon_intro zenon_H29. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H21. zenon_intro zenon_H2a. % 10.13/10.30 exact (zenon_H21 zenon_H1f). % 10.13/10.30 (* end of lemma zenon_L4_ *) % 10.13/10.30 assert (zenon_L5_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H2b. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H2f. zenon_intro zenon_H2e. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.13/10.30 exact (zenon_H30 zenon_H2d). % 10.13/10.30 (* end of lemma zenon_L5_ *) % 10.13/10.30 assert (zenon_L6_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H32. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H2d. zenon_intro zenon_H33. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H2f. zenon_intro zenon_H34. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 10.13/10.30 exact (zenon_H35 zenon_H36). % 10.13/10.30 (* end of lemma zenon_L6_ *) % 10.13/10.30 assert (zenon_L7_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H2d zenon_H1f zenon_H37. % 10.13/10.30 elim (classic ((op (e0) (e1)) = (op (e0) (e1)))); [ zenon_intro zenon_H38 | zenon_intro zenon_H39 ]. % 10.13/10.30 cut (((op (e0) (e1)) = (op (e0) (e1))) = ((op (e0) (e0)) = (op (e0) (e1)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H37. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H38. % 10.13/10.30 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 10.13/10.30 cut (((op (e0) (e1)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e0)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H3a. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H2d. % 10.13/10.30 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 10.13/10.30 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_H39. apply refl_equal. % 10.13/10.30 apply zenon_H3b. apply sym_equal. exact zenon_H1f. % 10.13/10.30 apply zenon_H39. apply refl_equal. % 10.13/10.30 apply zenon_H39. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L7_ *) % 10.13/10.30 assert (zenon_L8_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H3c zenon_H1f zenon_H37. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H2d. zenon_intro zenon_H3d. % 10.13/10.30 apply (zenon_L7_); trivial. % 10.13/10.30 (* end of lemma zenon_L8_ *) % 10.13/10.30 assert (zenon_L9_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H3e zenon_H1f zenon_H37. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H2d. zenon_intro zenon_H3f. % 10.13/10.30 apply (zenon_L7_); trivial. % 10.13/10.30 (* end of lemma zenon_L9_ *) % 10.13/10.30 assert (zenon_L10_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H40. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H41. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H43. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.13/10.30 exact (zenon_H45 zenon_H42). % 10.13/10.30 (* end of lemma zenon_L10_ *) % 10.13/10.30 assert (zenon_L11_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H42 zenon_H1f zenon_H47. % 10.13/10.30 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H48 | zenon_intro zenon_H49 ]. % 10.13/10.30 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e0)) = (op (e0) (e2)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H47. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H48. % 10.13/10.30 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 10.13/10.30 cut (((op (e0) (e2)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e0)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H4a. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H42. % 10.13/10.30 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 10.13/10.30 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_H49. apply refl_equal. % 10.13/10.30 apply zenon_H3b. apply sym_equal. exact zenon_H1f. % 10.13/10.30 apply zenon_H49. apply refl_equal. % 10.13/10.30 apply zenon_H49. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L11_ *) % 10.13/10.30 assert (zenon_L12_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H4b zenon_H1f zenon_H47. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H42. zenon_intro zenon_H4c. % 10.13/10.30 apply (zenon_L11_); trivial. % 10.13/10.30 (* end of lemma zenon_L12_ *) % 10.13/10.30 assert (zenon_L13_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H4d. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H42. zenon_intro zenon_H4e. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H44. zenon_intro zenon_H4f. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H50. % 10.13/10.30 exact (zenon_H50 zenon_H51). % 10.13/10.30 (* end of lemma zenon_L13_ *) % 10.13/10.30 assert (zenon_L14_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H52 zenon_H1f zenon_H47. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H42. zenon_intro zenon_H53. % 10.13/10.30 apply (zenon_L11_); trivial. % 10.13/10.30 (* end of lemma zenon_L14_ *) % 10.13/10.30 assert (zenon_L15_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H54. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H56. zenon_intro zenon_H55. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H58. zenon_intro zenon_H57. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.13/10.30 exact (zenon_H58 zenon_H5a). % 10.13/10.30 (* end of lemma zenon_L15_ *) % 10.13/10.30 assert (zenon_L16_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H56 zenon_H1f zenon_H5b. % 10.13/10.30 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 10.13/10.30 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e0)) = (op (e0) (e3)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H5b. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H5c. % 10.13/10.30 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.13/10.30 cut (((op (e0) (e3)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e0)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H5e. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H56. % 10.13/10.30 cut (((e0) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 10.13/10.30 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_H5d. apply refl_equal. % 10.13/10.30 apply zenon_H3b. apply sym_equal. exact zenon_H1f. % 10.13/10.30 apply zenon_H5d. apply refl_equal. % 10.13/10.30 apply zenon_H5d. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L16_ *) % 10.13/10.30 assert (zenon_L17_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H5f zenon_H1f zenon_H5b. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H56. zenon_intro zenon_H60. % 10.13/10.30 apply (zenon_L16_); trivial. % 10.13/10.30 (* end of lemma zenon_L17_ *) % 10.13/10.30 assert (zenon_L18_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H61 zenon_H1f zenon_H5b. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H56. zenon_intro zenon_H62. % 10.13/10.30 apply (zenon_L16_); trivial. % 10.13/10.30 (* end of lemma zenon_L18_ *) % 10.13/10.30 assert (zenon_L19_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H63. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H56. zenon_intro zenon_H64. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H58. zenon_intro zenon_H65. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 10.13/10.30 exact (zenon_H66 zenon_H67). % 10.13/10.30 (* end of lemma zenon_L19_ *) % 10.13/10.30 assert (zenon_L20_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H68. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H68). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6b. zenon_intro zenon_H20. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H1f. zenon_intro zenon_H21. % 10.13/10.30 exact (zenon_H21 zenon_H1f). % 10.13/10.30 (* end of lemma zenon_L20_ *) % 10.13/10.30 assert (zenon_L21_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H6c. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H6c). zenon_intro zenon_H6a. zenon_intro zenon_H6d. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H6d). zenon_intro zenon_H6b. zenon_intro zenon_H24. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.13/10.30 exact (zenon_H6e zenon_H6a). % 10.13/10.30 (* end of lemma zenon_L21_ *) % 10.13/10.30 assert (zenon_L22_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> (~((op (e2) (e2)) = (e0))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H70 zenon_H71. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H6a. zenon_intro zenon_H72. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H6b. zenon_intro zenon_H27. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.13/10.30 exact (zenon_H71 zenon_H74). % 10.13/10.30 (* end of lemma zenon_L22_ *) % 10.13/10.30 assert (zenon_L23_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H75 zenon_H76. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H6a. zenon_intro zenon_H77. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H6b. zenon_intro zenon_H2a. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.13/10.30 exact (zenon_H76 zenon_H79). % 10.13/10.30 (* end of lemma zenon_L23_ *) % 10.13/10.30 assert (zenon_L24_ : (((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H7a. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H7a). zenon_intro zenon_H36. zenon_intro zenon_H7b. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H7b). zenon_intro zenon_H35. zenon_intro zenon_H2e. % 10.13/10.30 exact (zenon_H35 zenon_H36). % 10.13/10.30 (* end of lemma zenon_L24_ *) % 10.13/10.30 assert (zenon_L25_ : (((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H7c. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H7c). zenon_intro zenon_H36. zenon_intro zenon_H7d. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H35. zenon_intro zenon_H34. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 10.13/10.30 exact (zenon_H35 zenon_H36). % 10.13/10.30 (* end of lemma zenon_L25_ *) % 10.13/10.30 assert (zenon_L26_ : (((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H7e. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H7e). zenon_intro zenon_H36. zenon_intro zenon_H7f. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H7f). zenon_intro zenon_H35. zenon_intro zenon_H80. % 10.13/10.30 exact (zenon_H35 zenon_H36). % 10.13/10.30 (* end of lemma zenon_L26_ *) % 10.13/10.30 assert (zenon_L27_ : (((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H81. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H81). zenon_intro zenon_H36. zenon_intro zenon_H82. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H82). zenon_intro zenon_H35. zenon_intro zenon_H83. % 10.13/10.30 exact (zenon_H35 zenon_H36). % 10.13/10.30 (* end of lemma zenon_L27_ *) % 10.13/10.30 assert (zenon_L28_ : (~((e0) = (e0))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H84. % 10.13/10.30 apply zenon_H84. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L28_ *) % 10.13/10.30 assert (zenon_L29_ : ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H1f zenon_H46 zenon_H85. % 10.13/10.30 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.13/10.30 cut (((e2) = (e2)) = ((e0) = (e2))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H85. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H86. % 10.13/10.30 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.30 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e0) (e0)) = (e0)) = ((e2) = (e0))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H88. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H1f. % 10.13/10.30 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.30 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_H44 zenon_H46). % 10.13/10.30 apply zenon_H84. apply refl_equal. % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L29_ *) % 10.13/10.30 assert (zenon_L30_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H89 zenon_H1f zenon_H85. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8c. zenon_intro zenon_H43. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.13/10.30 apply (zenon_L29_); trivial. % 10.13/10.30 (* end of lemma zenon_L30_ *) % 10.13/10.30 assert (zenon_L31_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H8d. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H8b. zenon_intro zenon_H8e. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H8c. zenon_intro zenon_H8f. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.13/10.30 exact (zenon_H90 zenon_H8b). % 10.13/10.30 (* end of lemma zenon_L31_ *) % 10.13/10.30 assert (zenon_L32_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H92. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H8b. zenon_intro zenon_H93. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H93). zenon_intro zenon_H8c. zenon_intro zenon_H4f. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H50. % 10.13/10.30 exact (zenon_H50 zenon_H51). % 10.13/10.30 (* end of lemma zenon_L32_ *) % 10.13/10.30 assert (zenon_L33_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H94 zenon_H1f zenon_H95. % 10.13/10.30 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H94. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H1f. % 10.13/10.30 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 10.13/10.30 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_H97. apply refl_equal. % 10.13/10.30 apply zenon_H96. apply sym_equal. exact zenon_H95. % 10.13/10.30 (* end of lemma zenon_L33_ *) % 10.13/10.30 assert (zenon_L34_ : (~((e1) = (e1))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H98. % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L34_ *) % 10.13/10.30 assert (zenon_L35_ : (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H99 zenon_H8b zenon_H9a. % 10.13/10.30 cut (((op (e1) (e2)) = (e1)) = ((e0) = (e1))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H99. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H8b. % 10.13/10.30 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.30 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_H9b zenon_H9a). % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L35_ *) % 10.13/10.30 assert (zenon_L36_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H8b zenon_H36 zenon_H9c. % 10.13/10.30 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H9d | zenon_intro zenon_H9e ]. % 10.13/10.30 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e1)) = (op (e1) (e2)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H9c. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H9d. % 10.13/10.30 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 10.13/10.30 cut (((op (e1) (e2)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e1)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H9f. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H8b. % 10.13/10.30 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 10.13/10.30 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_H9e. apply refl_equal. % 10.13/10.30 apply zenon_Ha0. apply sym_equal. exact zenon_H36. % 10.13/10.30 apply zenon_H9e. apply refl_equal. % 10.13/10.30 apply zenon_H9e. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L36_ *) % 10.13/10.30 assert (zenon_L37_ : (~((op (e1) (op (e1) (e1))) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Ha1 zenon_Ha2. % 10.13/10.30 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 10.13/10.30 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.30 (* end of lemma zenon_L37_ *) % 10.13/10.30 assert (zenon_L38_ : (~((e2) = (e2))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H87. % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L38_ *) % 10.13/10.30 assert (zenon_L39_ : ((op (e0) (e1)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (op (op (e1) (op (e1) (e1))) (e1)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Ha4 zenon_Ha5 zenon_Ha2 zenon_Ha6. % 10.13/10.30 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((e2) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Ha6. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Ha7. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e0) (e1)) = (e2)) = ((op (op (e1) (op (e1) (e1))) (e1)) = (e2))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Ha9. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Ha4. % 10.13/10.30 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.30 cut (((op (e0) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 10.13/10.30 congruence. % 10.13/10.30 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((op (e0) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Haa. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Ha7. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (op (e1) (e1))) = (e0))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hac. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Ha5. % 10.13/10.30 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.30 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 10.13/10.30 congruence. % 10.13/10.30 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e3)) = (op (e1) (op (e1) (e1))))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Had. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hae. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 10.13/10.30 congruence. % 10.13/10.30 apply (zenon_L37_); trivial. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply zenon_H84. apply refl_equal. % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 apply zenon_Ha8. apply refl_equal. % 10.13/10.30 apply zenon_Ha8. apply refl_equal. % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 apply zenon_Ha8. apply refl_equal. % 10.13/10.30 apply zenon_Ha8. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L39_ *) % 10.13/10.30 assert (zenon_L40_ : ((op (e0) (e1)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Ha4 zenon_Ha5 zenon_Ha2. % 10.13/10.30 apply (zenon_notand_s _ _ ax16); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb0 ]. % 10.13/10.30 apply zenon_Hb1. apply sym_equal. exact zenon_Ha2. % 10.13/10.30 apply (zenon_notand_s _ _ zenon_Hb0); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Ha6 ]. % 10.13/10.30 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((e0) = (op (e1) (op (e1) (e1))))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hb2. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hae. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (op (e1) (e1))) = (e0))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hac. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Ha5. % 10.13/10.30 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.30 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 10.13/10.30 congruence. % 10.13/10.30 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e3)) = (op (e1) (op (e1) (e1))))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Had. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hae. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 10.13/10.30 congruence. % 10.13/10.30 apply (zenon_L37_); trivial. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply zenon_H84. apply refl_equal. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply (zenon_L39_); trivial. % 10.13/10.30 (* end of lemma zenon_L40_ *) % 10.13/10.30 assert (zenon_L41_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e3)) = (e0)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hb3 zenon_H6b zenon_H9c zenon_H8b zenon_H8c zenon_Ha4 zenon_Ha5. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.13/10.30 exact (zenon_H6b zenon_H6f). % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.13/10.30 apply (zenon_L36_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.13/10.30 exact (zenon_H8c zenon_H91). % 10.13/10.30 apply (zenon_L40_); trivial. % 10.13/10.30 (* end of lemma zenon_L41_ *) % 10.13/10.30 assert (zenon_L42_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e2)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hb6 zenon_H1f zenon_H94 zenon_H99 zenon_Hb3 zenon_H6b zenon_H9c zenon_H8b zenon_H8c zenon_Ha4. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.30 apply (zenon_L33_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.30 exact (zenon_H6b zenon_H6f). % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.30 apply (zenon_L35_); trivial. % 10.13/10.30 apply (zenon_L41_); trivial. % 10.13/10.30 (* end of lemma zenon_L42_ *) % 10.13/10.30 assert (zenon_L43_ : ((op (e2) (e0)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hb9 zenon_Hba zenon_Hbb. % 10.13/10.30 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbd ]. % 10.13/10.30 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e1) (e0)) = (op (e2) (e0)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hbb. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hbc. % 10.13/10.30 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 10.13/10.30 cut (((op (e2) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e1) (e0)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hbe. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hb9. % 10.13/10.30 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 10.13/10.30 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_Hbd. apply refl_equal. % 10.13/10.30 apply zenon_Hbf. apply sym_equal. exact zenon_Hba. % 10.13/10.30 apply zenon_Hbd. apply refl_equal. % 10.13/10.30 apply zenon_Hbd. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L43_ *) % 10.13/10.30 assert (zenon_L44_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hc0 zenon_H1f zenon_Hc1. % 10.13/10.30 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hc0. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H1f. % 10.13/10.30 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hc2]. % 10.13/10.30 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_H97. apply refl_equal. % 10.13/10.30 apply zenon_Hc2. apply sym_equal. exact zenon_Hc1. % 10.13/10.30 (* end of lemma zenon_L44_ *) % 10.13/10.30 assert (zenon_L45_ : (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H85 zenon_Hc3 zenon_Hc4. % 10.13/10.30 cut (((op (e2) (e1)) = (e2)) = ((e0) = (e2))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H85. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hc3. % 10.13/10.30 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.30 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_Hc5 zenon_Hc4). % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L45_ *) % 10.13/10.30 assert (zenon_L46_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hc6 zenon_Ha5 zenon_Hc7. % 10.13/10.30 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hc6. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Ha5. % 10.13/10.30 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 10.13/10.30 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_Hc9. apply refl_equal. % 10.13/10.30 apply zenon_Hc8. apply sym_equal. exact zenon_Hc7. % 10.13/10.30 (* end of lemma zenon_L46_ *) % 10.13/10.30 assert (zenon_L47_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e0)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hca zenon_H1f zenon_Hc0 zenon_Hc3 zenon_H85 zenon_H71 zenon_Hc6 zenon_Ha5. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.13/10.30 apply (zenon_L44_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.13/10.30 apply (zenon_L45_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.13/10.30 exact (zenon_H71 zenon_H74). % 10.13/10.30 apply (zenon_L46_); trivial. % 10.13/10.30 (* end of lemma zenon_L47_ *) % 10.13/10.30 assert (zenon_L48_ : ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H51 zenon_Hcd zenon_Hce. % 10.13/10.30 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd0 ]. % 10.13/10.30 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hce. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hcf. % 10.13/10.30 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.30 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hd1. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H51. % 10.13/10.30 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 10.13/10.30 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_Hd0. apply refl_equal. % 10.13/10.30 apply zenon_Hd2. apply sym_equal. exact zenon_Hcd. % 10.13/10.30 apply zenon_Hd0. apply refl_equal. % 10.13/10.30 apply zenon_Hd0. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L48_ *) % 10.13/10.30 assert (zenon_L49_ : ((op (e3) (e3)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hd3 zenon_Hd4 zenon_Hd5. % 10.13/10.30 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.13/10.30 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hd5. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hd6. % 10.13/10.30 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.30 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hd8. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hd3. % 10.13/10.30 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 10.13/10.30 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_Hd7. apply refl_equal. % 10.13/10.30 apply zenon_Hd9. apply sym_equal. exact zenon_Hd4. % 10.13/10.30 apply zenon_Hd7. apply refl_equal. % 10.13/10.30 apply zenon_Hd7. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L49_ *) % 10.13/10.30 assert (zenon_L50_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hda zenon_Hcd zenon_Hdb. % 10.13/10.30 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hda. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hcd. % 10.13/10.30 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 10.13/10.30 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_H49. apply refl_equal. % 10.13/10.30 apply zenon_Hdc. apply sym_equal. exact zenon_Hdb. % 10.13/10.30 (* end of lemma zenon_L50_ *) % 10.13/10.30 assert (zenon_L51_ : ((op (e1) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Ha5 zenon_Hdd zenon_H85. % 10.13/10.30 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.13/10.30 cut (((e2) = (e2)) = ((e0) = (e2))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H85. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H86. % 10.13/10.30 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.30 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e1) (e3)) = (e0)) = ((e2) = (e0))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H88. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Ha5. % 10.13/10.30 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.30 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_Hde zenon_Hdd). % 10.13/10.30 apply zenon_H84. apply refl_equal. % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L51_ *) % 10.13/10.30 assert (zenon_L52_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hb6 zenon_H94 zenon_H6b zenon_H8b zenon_H99 zenon_Hdf zenon_Hd5 zenon_Hd3 zenon_Hce zenon_Hca zenon_H1f zenon_Hc0 zenon_H71 zenon_Hc6 zenon_Hbb zenon_He0 zenon_H8c zenon_Hcd zenon_Hda zenon_H85. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.30 apply (zenon_L33_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.30 exact (zenon_H6b zenon_H6f). % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.30 apply (zenon_L35_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.13/10.30 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.30 apply (zenon_L43_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.30 apply (zenon_L47_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.30 apply (zenon_L48_); trivial. % 10.13/10.30 apply (zenon_L49_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.13/10.30 exact (zenon_H8c zenon_H91). % 10.13/10.30 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.13/10.30 apply (zenon_L50_); trivial. % 10.13/10.30 apply (zenon_L51_); trivial. % 10.13/10.30 (* end of lemma zenon_L52_ *) % 10.13/10.30 assert (zenon_L53_ : ((op (e3) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hd3 zenon_He5 zenon_He6. % 10.13/10.30 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.13/10.30 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_He6. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hd6. % 10.13/10.30 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.30 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e3) (e3)) = (e2)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_He7. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hd3. % 10.13/10.30 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 10.13/10.30 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_Hd7. apply refl_equal. % 10.13/10.30 apply zenon_He8. apply sym_equal. exact zenon_He5. % 10.13/10.30 apply zenon_Hd7. apply refl_equal. % 10.13/10.30 apply zenon_Hd7. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L53_ *) % 10.13/10.30 assert (zenon_L54_ : ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H1f zenon_H5a zenon_He9. % 10.13/10.30 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.30 cut (((e3) = (e3)) = ((e0) = (e3))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_He9. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hea. % 10.13/10.30 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.30 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e0) (e0)) = (e0)) = ((e3) = (e0))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hec. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H1f. % 10.13/10.30 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.30 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_H58 zenon_H5a). % 10.13/10.30 apply zenon_H84. apply refl_equal. % 10.13/10.30 apply zenon_Heb. apply refl_equal. % 10.13/10.30 apply zenon_Heb. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L54_ *) % 10.13/10.30 assert (zenon_L55_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hed zenon_H1f zenon_He9. % 10.13/10.30 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hef. zenon_intro zenon_Hee. % 10.13/10.30 apply (zenon_and_s _ _ zenon_Hee). zenon_intro zenon_Ha3. zenon_intro zenon_H57. % 10.13/10.30 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.13/10.30 apply (zenon_L54_); trivial. % 10.13/10.30 (* end of lemma zenon_L55_ *) % 10.13/10.30 assert (zenon_L56_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hf0. % 10.13/10.30 apply (zenon_and_s _ _ zenon_Hf0). zenon_intro zenon_Hef. zenon_intro zenon_Hf1. % 10.13/10.30 apply (zenon_and_s _ _ zenon_Hf1). zenon_intro zenon_Ha3. zenon_intro zenon_Hf2. % 10.13/10.30 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.13/10.30 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.30 (* end of lemma zenon_L56_ *) % 10.13/10.30 assert (zenon_L57_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H31 zenon_H46 zenon_Hf4. % 10.13/10.30 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.13/10.30 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hf4. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H86. % 10.13/10.30 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.30 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e0) (e0)) = (e1)) = ((e2) = (e1))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hf5. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H31. % 10.13/10.30 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.30 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_H44 zenon_H46). % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L57_ *) % 10.13/10.30 assert (zenon_L58_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H2d zenon_Hf6 zenon_H99. % 10.13/10.30 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H98 ]. % 10.13/10.30 cut (((e1) = (e1)) = ((e0) = (e1))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H99. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hf7. % 10.13/10.30 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.30 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e0) (e1)) = (e0)) = ((e1) = (e0))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hf8. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H2d. % 10.13/10.30 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.30 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_Hf9 zenon_Hf6). % 10.13/10.30 apply zenon_H84. apply refl_equal. % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L58_ *) % 10.13/10.30 assert (zenon_L59_ : (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hf4 zenon_Hb9 zenon_Hfa. % 10.13/10.30 cut (((op (e2) (e0)) = (e2)) = ((e1) = (e2))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hf4. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hb9. % 10.13/10.30 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.30 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_Hfb zenon_Hfa). % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L59_ *) % 10.13/10.30 assert (zenon_L60_ : ((op (e2) (e2)) = (e2)) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H51 zenon_Hfc zenon_Hfd. % 10.13/10.30 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.30 cut (((e3) = (e3)) = ((e2) = (e3))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hfd. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hea. % 10.13/10.30 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.30 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e2) (e2)) = (e2)) = ((e3) = (e2))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hfe. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H51. % 10.13/10.30 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.30 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_Hff zenon_Hfc). % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 apply zenon_Heb. apply refl_equal. % 10.13/10.30 apply zenon_Heb. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L60_ *) % 10.13/10.30 assert (zenon_L61_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H100 zenon_Hf6 zenon_H101. % 10.13/10.30 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H100. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hf6. % 10.13/10.30 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 10.13/10.30 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_H39. apply refl_equal. % 10.13/10.30 apply zenon_H102. apply sym_equal. exact zenon_H101. % 10.13/10.30 (* end of lemma zenon_L61_ *) % 10.13/10.30 assert (zenon_L62_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H103 zenon_Hfc zenon_H104. % 10.13/10.30 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.30 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H104. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hea. % 10.13/10.30 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.30 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e2) (e2)) = (e1)) = ((e3) = (e1))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H105. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H103. % 10.13/10.30 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.30 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_Hff zenon_Hfc). % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 apply zenon_Heb. apply refl_equal. % 10.13/10.30 apply zenon_Heb. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L62_ *) % 10.13/10.30 assert (zenon_L63_ : (~((op (e2) (op (e2) (e2))) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H106 zenon_Hfc. % 10.13/10.30 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 10.13/10.30 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 exact (zenon_Hff zenon_Hfc). % 10.13/10.30 (* end of lemma zenon_L63_ *) % 10.13/10.30 assert (zenon_L64_ : ((op (e1) (e2)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H9a zenon_H107 zenon_Hfc. % 10.13/10.30 apply (zenon_notand_s _ _ ax23); [ zenon_intro zenon_H109 | zenon_intro zenon_H108 ]. % 10.13/10.30 apply zenon_H109. apply sym_equal. exact zenon_Hfc. % 10.13/10.30 apply (zenon_notand_s _ _ zenon_H108); [ zenon_intro zenon_H10b | zenon_intro zenon_H10a ]. % 10.13/10.30 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.13/10.30 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((e1) = (op (e2) (op (e2) (e2))))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H10b. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H10c. % 10.13/10.30 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.13/10.30 cut (((op (e2) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e2) (e3)) = (e1)) = ((op (e2) (op (e2) (e2))) = (e1))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H10e. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H107. % 10.13/10.30 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.30 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 10.13/10.30 congruence. % 10.13/10.30 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.13/10.30 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e3)) = (op (e2) (op (e2) (e2))))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H10f. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H10c. % 10.13/10.30 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.13/10.30 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 10.13/10.30 congruence. % 10.13/10.30 apply (zenon_L63_); trivial. % 10.13/10.30 apply zenon_H10d. apply refl_equal. % 10.13/10.30 apply zenon_H10d. apply refl_equal. % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 apply zenon_H10d. apply refl_equal. % 10.13/10.30 apply zenon_H10d. apply refl_equal. % 10.13/10.30 elim (classic ((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 10.13/10.30 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2))) = ((e0) = (op (op (e2) (op (e2) (e2))) (e2)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H10a. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H110. % 10.13/10.30 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 10.13/10.30 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e1) (e2)) = (e0)) = ((op (op (e2) (op (e2) (e2))) (e2)) = (e0))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H112. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H9a. % 10.13/10.30 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.30 cut (((op (e1) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 10.13/10.30 congruence. % 10.13/10.30 elim (classic ((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 10.13/10.30 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2))) = ((op (e1) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H113. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H110. % 10.13/10.30 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 10.13/10.30 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.30 cut (((op (e2) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e2) (e3)) = (e1)) = ((op (e2) (op (e2) (e2))) = (e1))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H10e. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H107. % 10.13/10.30 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.30 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 10.13/10.30 congruence. % 10.13/10.30 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.13/10.30 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e3)) = (op (e2) (op (e2) (e2))))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H10f. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H10c. % 10.13/10.30 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.13/10.30 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 10.13/10.30 congruence. % 10.13/10.30 apply (zenon_L63_); trivial. % 10.13/10.30 apply zenon_H10d. apply refl_equal. % 10.13/10.30 apply zenon_H10d. apply refl_equal. % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 apply zenon_H111. apply refl_equal. % 10.13/10.30 apply zenon_H111. apply refl_equal. % 10.13/10.30 apply zenon_H84. apply refl_equal. % 10.13/10.30 apply zenon_H111. apply refl_equal. % 10.13/10.30 apply zenon_H111. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L64_ *) % 10.13/10.30 assert (zenon_L65_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hef zenon_H36 zenon_H115. % 10.13/10.30 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H116 | zenon_intro zenon_Hc9 ]. % 10.13/10.30 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e1)) = (op (e1) (e3)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H115. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H116. % 10.13/10.30 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 10.13/10.30 cut (((op (e1) (e3)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e1)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H117. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hef. % 10.13/10.30 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 10.13/10.30 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_Hc9. apply refl_equal. % 10.13/10.30 apply zenon_Ha0. apply sym_equal. exact zenon_H36. % 10.13/10.30 apply zenon_Hc9. apply refl_equal. % 10.13/10.30 apply zenon_Hc9. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L65_ *) % 10.13/10.30 assert (zenon_L66_ : (~((op (e1) (op (e1) (e1))) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e2)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H118 zenon_H91. % 10.13/10.30 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 10.13/10.30 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 exact (zenon_H8c zenon_H91). % 10.13/10.30 (* end of lemma zenon_L66_ *) % 10.13/10.30 assert (zenon_L67_ : (~((e3) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Heb. % 10.13/10.30 apply zenon_Heb. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L67_ *) % 10.13/10.30 assert (zenon_L68_ : ((op (e0) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e3) = (op (op (e1) (op (e1) (e1))) (e1)))) -> False). % 10.13/10.30 do 0 intro. intros zenon_H119 zenon_H9a zenon_H91 zenon_H11a. % 10.13/10.30 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((e3) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H11a. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Ha7. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e0) (e1)) = (e3)) = ((op (op (e1) (op (e1) (e1))) (e1)) = (e3))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H11b. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H119. % 10.13/10.30 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.30 cut (((op (e0) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 10.13/10.30 congruence. % 10.13/10.30 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((op (e0) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Haa. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Ha7. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.13/10.30 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (op (e1) (e1))) = (e0))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hac. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H9a. % 10.13/10.30 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.30 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 10.13/10.30 congruence. % 10.13/10.30 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e1) (e1))))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H11c. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hae. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 10.13/10.30 congruence. % 10.13/10.30 apply (zenon_L66_); trivial. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply zenon_H84. apply refl_equal. % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 apply zenon_Ha8. apply refl_equal. % 10.13/10.30 apply zenon_Ha8. apply refl_equal. % 10.13/10.30 apply zenon_Heb. apply refl_equal. % 10.13/10.30 apply zenon_Ha8. apply refl_equal. % 10.13/10.30 apply zenon_Ha8. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L68_ *) % 10.13/10.30 assert (zenon_L69_ : ((op (e0) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H119 zenon_H9a zenon_H91. % 10.13/10.30 apply (zenon_notand_s _ _ ax14); [ zenon_intro zenon_H11e | zenon_intro zenon_H11d ]. % 10.13/10.30 apply zenon_H11e. apply sym_equal. exact zenon_H91. % 10.13/10.30 apply (zenon_notand_s _ _ zenon_H11d); [ zenon_intro zenon_Hb2 | zenon_intro zenon_H11a ]. % 10.13/10.30 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((e0) = (op (e1) (op (e1) (e1))))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hb2. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hae. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (op (e1) (e1))) = (e0))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hac. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H9a. % 10.13/10.30 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.30 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 10.13/10.30 congruence. % 10.13/10.30 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e1) (e1))))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H11c. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hae. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.30 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 10.13/10.30 congruence. % 10.13/10.30 apply (zenon_L66_); trivial. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply zenon_H84. apply refl_equal. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply zenon_Haf. apply refl_equal. % 10.13/10.30 apply (zenon_L68_); trivial. % 10.13/10.30 (* end of lemma zenon_L69_ *) % 10.13/10.30 assert (zenon_L70_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hb3 zenon_H6b zenon_H115 zenon_Hef zenon_H9a zenon_H119 zenon_Ha3. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.13/10.30 exact (zenon_H6b zenon_H6f). % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.13/10.30 apply (zenon_L65_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.13/10.30 apply (zenon_L69_); trivial. % 10.13/10.30 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.30 (* end of lemma zenon_L70_ *) % 10.13/10.30 assert (zenon_L71_ : (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H99 zenon_Hef zenon_Ha5. % 10.13/10.30 cut (((op (e1) (e3)) = (e1)) = ((e0) = (e1))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_H99. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hef. % 10.13/10.30 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.30 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H11f]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_H11f zenon_Ha5). % 10.13/10.30 apply zenon_H98. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L71_ *) % 10.13/10.30 assert (zenon_L72_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hb6 zenon_H1f zenon_H94 zenon_Ha3 zenon_H119 zenon_H115 zenon_H6b zenon_Hb3 zenon_H99 zenon_Hef. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.30 apply (zenon_L33_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.30 exact (zenon_H6b zenon_H6f). % 10.13/10.30 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.30 apply (zenon_L70_); trivial. % 10.13/10.30 apply (zenon_L71_); trivial. % 10.13/10.30 (* end of lemma zenon_L72_ *) % 10.13/10.30 assert (zenon_L73_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hc3 zenon_H120 zenon_Hfd. % 10.13/10.30 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.30 cut (((e3) = (e3)) = ((e2) = (e3))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hfd. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hea. % 10.13/10.30 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.30 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 10.13/10.30 congruence. % 10.13/10.30 cut (((op (e2) (e1)) = (e2)) = ((e3) = (e2))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hfe. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hc3. % 10.13/10.30 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.30 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_H121 zenon_H120). % 10.13/10.30 apply zenon_H87. apply refl_equal. % 10.13/10.30 apply zenon_Heb. apply refl_equal. % 10.13/10.30 apply zenon_Heb. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L73_ *) % 10.13/10.30 assert (zenon_L74_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e3)) = (e2))) -> False). % 10.13/10.30 do 0 intro. intros zenon_He0 zenon_Hfa zenon_Hf4 zenon_H120 zenon_Hfd zenon_Hfc zenon_H122. % 10.13/10.30 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.30 apply (zenon_L59_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.30 apply (zenon_L73_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.30 apply (zenon_L60_); trivial. % 10.13/10.30 exact (zenon_H122 zenon_Hd4). % 10.13/10.30 (* end of lemma zenon_L74_ *) % 10.13/10.30 assert (zenon_L75_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 10.13/10.30 do 0 intro. intros zenon_Hc6 zenon_Hef zenon_H107. % 10.13/10.30 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_Hc6. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_Hef. % 10.13/10.30 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 10.13/10.30 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 10.13/10.30 congruence. % 10.13/10.30 apply zenon_Hc9. apply refl_equal. % 10.13/10.30 apply zenon_H123. apply sym_equal. exact zenon_H107. % 10.13/10.30 (* end of lemma zenon_L75_ *) % 10.13/10.30 assert (zenon_L76_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H124 zenon_H122 zenon_Hfd zenon_H120 zenon_Hf4 zenon_He0 zenon_Hf6 zenon_H100 zenon_H104 zenon_Hfc zenon_Hc6 zenon_Hef. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.30 apply (zenon_L74_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.30 apply (zenon_L61_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.30 apply (zenon_L62_); trivial. % 10.13/10.30 apply (zenon_L75_); trivial. % 10.13/10.30 (* end of lemma zenon_L76_ *) % 10.13/10.30 assert (zenon_L77_ : (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> False). % 10.13/10.30 do 0 intro. intros zenon_He9 zenon_H127 zenon_H128. % 10.13/10.30 cut (((op (e3) (e1)) = (e3)) = ((e0) = (e3))). % 10.13/10.30 intro zenon_D_pnotp. % 10.13/10.30 apply zenon_He9. % 10.13/10.30 rewrite <- zenon_D_pnotp. % 10.13/10.30 exact zenon_H127. % 10.13/10.30 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.30 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H129]. % 10.13/10.30 congruence. % 10.13/10.30 exact (zenon_H129 zenon_H128). % 10.13/10.30 apply zenon_Heb. apply refl_equal. % 10.13/10.30 (* end of lemma zenon_L77_ *) % 10.13/10.30 assert (zenon_L78_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> False). % 10.13/10.30 do 0 intro. intros zenon_H12a zenon_H99 zenon_Hb3 zenon_H6b zenon_H115 zenon_H94 zenon_H1f zenon_Hb6 zenon_Ha3 zenon_Hef zenon_Hc6 zenon_Hfc zenon_H104 zenon_H100 zenon_Hf6 zenon_He0 zenon_Hf4 zenon_Hfd zenon_H122 zenon_H124 zenon_He9 zenon_H128. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.13/10.30 apply (zenon_L72_); trivial. % 10.13/10.30 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.13/10.30 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.30 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.13/10.30 apply (zenon_L76_); trivial. % 10.13/10.30 apply (zenon_L77_); trivial. % 10.13/10.30 (* end of lemma zenon_L78_ *) % 10.13/10.30 assert (zenon_L79_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H12d zenon_H9a zenon_H85 zenon_H12a zenon_H99 zenon_Hb3 zenon_H6b zenon_H115 zenon_H94 zenon_H1f zenon_Hb6 zenon_Ha3 zenon_Hef zenon_Hc6 zenon_Hfc zenon_H104 zenon_H100 zenon_Hf6 zenon_He0 zenon_Hf4 zenon_Hfd zenon_H122 zenon_H124 zenon_He9. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.31 apply (zenon_L58_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.31 apply (zenon_L59_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.31 apply (zenon_L45_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.31 apply (zenon_L60_); trivial. % 10.13/10.31 exact (zenon_H122 zenon_Hd4). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.31 apply (zenon_L61_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.31 apply (zenon_L62_); trivial. % 10.13/10.31 apply (zenon_L64_); trivial. % 10.13/10.31 apply (zenon_L78_); trivial. % 10.13/10.31 (* end of lemma zenon_L79_ *) % 10.13/10.31 assert (zenon_L80_ : (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_He9 zenon_H124 zenon_H122 zenon_Hfd zenon_Hf4 zenon_He0 zenon_Hf6 zenon_H100 zenon_H104 zenon_Hfc zenon_Hc6 zenon_Ha3 zenon_Hb6 zenon_H1f zenon_H94 zenon_H115 zenon_H6b zenon_Hb3 zenon_H12a zenon_H85 zenon_H12d zenon_H99 zenon_Hef. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.31 apply (zenon_L33_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.31 apply (zenon_L79_); trivial. % 10.13/10.31 apply (zenon_L71_); trivial. % 10.13/10.31 (* end of lemma zenon_L80_ *) % 10.13/10.31 assert (zenon_L81_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H130 zenon_H1f zenon_H131. % 10.13/10.31 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H130. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H1f. % 10.13/10.31 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 10.13/10.31 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H97. apply refl_equal. % 10.13/10.31 apply zenon_H132. apply sym_equal. exact zenon_H131. % 10.13/10.31 (* end of lemma zenon_L81_ *) % 10.13/10.31 assert (zenon_L82_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H130 zenon_H31 zenon_H133. % 10.13/10.31 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H130. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H31. % 10.13/10.31 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 10.13/10.31 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H97. apply refl_equal. % 10.13/10.31 apply zenon_H134. apply sym_equal. exact zenon_H133. % 10.13/10.31 (* end of lemma zenon_L82_ *) % 10.13/10.31 assert (zenon_L83_ : (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H135 zenon_Hb9 zenon_H136. % 10.13/10.31 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e3) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H135. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hb9. % 10.13/10.31 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 10.13/10.31 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_Hbd. apply refl_equal. % 10.13/10.31 apply zenon_H137. apply sym_equal. exact zenon_H136. % 10.13/10.31 (* end of lemma zenon_L83_ *) % 10.13/10.31 assert (zenon_L84_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hef zenon_H6a zenon_H138. % 10.13/10.31 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H116 | zenon_intro zenon_Hc9 ]. % 10.13/10.31 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e0)) = (op (e1) (e3)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H138. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H116. % 10.13/10.31 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 10.13/10.31 cut (((op (e1) (e3)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H139. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hef. % 10.13/10.31 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 10.13/10.31 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_Hc9. apply refl_equal. % 10.13/10.31 apply zenon_H13a. apply sym_equal. exact zenon_H6a. % 10.13/10.31 apply zenon_Hc9. apply refl_equal. % 10.13/10.31 apply zenon_Hc9. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L84_ *) % 10.13/10.31 assert (zenon_L85_ : ((op (e3) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H13b zenon_H13c zenon_H13d. % 10.13/10.31 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 10.13/10.31 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e1) (e0)) = (op (e3) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H13d. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H13e. % 10.13/10.31 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 10.13/10.31 cut (((op (e3) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e1) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H140. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H13b. % 10.13/10.31 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 10.13/10.31 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H13f. apply refl_equal. % 10.13/10.31 apply zenon_H141. apply sym_equal. exact zenon_H13c. % 10.13/10.31 apply zenon_H13f. apply refl_equal. % 10.13/10.31 apply zenon_H13f. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L85_ *) % 10.13/10.31 assert (zenon_L86_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H142 zenon_H1f zenon_H94 zenon_H138 zenon_Hef zenon_Hbb zenon_Hb9 zenon_H13b zenon_H13d. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H95 | zenon_intro zenon_H143 ]. % 10.13/10.31 apply (zenon_L33_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H6a | zenon_intro zenon_H144 ]. % 10.13/10.31 apply (zenon_L84_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hba | zenon_intro zenon_H13c ]. % 10.13/10.31 apply (zenon_L43_); trivial. % 10.13/10.31 apply (zenon_L85_); trivial. % 10.13/10.31 (* end of lemma zenon_L86_ *) % 10.13/10.31 assert (zenon_L87_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H145 zenon_H31 zenon_H130 zenon_H135 zenon_H142 zenon_H1f zenon_H94 zenon_H138 zenon_Hef zenon_Hbb zenon_Hb9 zenon_H13d. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H131 | zenon_intro zenon_H146 ]. % 10.13/10.31 apply (zenon_L81_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H133 | zenon_intro zenon_H147 ]. % 10.13/10.31 apply (zenon_L82_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H136 | zenon_intro zenon_H13b ]. % 10.13/10.31 apply (zenon_L83_); trivial. % 10.13/10.31 apply (zenon_L86_); trivial. % 10.13/10.31 (* end of lemma zenon_L87_ *) % 10.13/10.31 assert (zenon_L88_ : ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hb9 zenon_H46 zenon_Hc0. % 10.13/10.31 elim (classic ((op (e2) (e0)) = (op (e2) (e0)))); [ zenon_intro zenon_Hbc | zenon_intro zenon_Hbd ]. % 10.13/10.31 cut (((op (e2) (e0)) = (op (e2) (e0))) = ((op (e0) (e0)) = (op (e2) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hc0. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hbc. % 10.13/10.31 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 10.13/10.31 cut (((op (e2) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e0) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H148. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hb9. % 10.13/10.31 cut (((e2) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 10.13/10.31 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_Hbd. apply refl_equal. % 10.13/10.31 apply zenon_H149. apply sym_equal. exact zenon_H46. % 10.13/10.31 apply zenon_Hbd. apply refl_equal. % 10.13/10.31 apply zenon_Hbd. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L88_ *) % 10.13/10.31 assert (zenon_L89_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hf6 zenon_Ha4 zenon_Hf4. % 10.13/10.31 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.13/10.31 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hf4. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H86. % 10.13/10.31 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.31 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e0) (e1)) = (e1)) = ((e2) = (e1))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hf5. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hf6. % 10.13/10.31 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.31 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H14a zenon_Ha4). % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L89_ *) % 10.13/10.31 assert (zenon_L90_ : ((op (e3) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H127 zenon_H119 zenon_H14b. % 10.13/10.31 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H14c | zenon_intro zenon_H14d ]. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e0) (e1)) = (op (e3) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H14b. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H14c. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14e]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e0) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H14e. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H127. % 10.13/10.31 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H14d. apply refl_equal. % 10.13/10.31 apply zenon_H14f. apply sym_equal. exact zenon_H119. % 10.13/10.31 apply zenon_H14d. apply refl_equal. % 10.13/10.31 apply zenon_H14d. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L90_ *) % 10.13/10.31 assert (zenon_L91_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hcd zenon_H150 zenon_Hfd. % 10.13/10.31 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.31 cut (((e3) = (e3)) = ((e2) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hfd. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hea. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e0) (e2)) = (e2)) = ((e3) = (e2))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hfe. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hcd. % 10.13/10.31 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.31 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H151 zenon_H150). % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L91_ *) % 10.13/10.31 assert (zenon_L92_ : ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hb9 zenon_H152 zenon_Hfd. % 10.13/10.31 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.31 cut (((e3) = (e3)) = ((e2) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hfd. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hea. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e2) (e0)) = (e2)) = ((e3) = (e2))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hfe. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hb9. % 10.13/10.31 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.31 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H153 zenon_H152). % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L92_ *) % 10.13/10.31 assert (zenon_L93_ : ((op (e3) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H127 zenon_H120 zenon_H154. % 10.13/10.31 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H14c | zenon_intro zenon_H14d ]. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H154. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H14c. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H155. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H127. % 10.13/10.31 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H156]. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H14d. apply refl_equal. % 10.13/10.31 apply zenon_H156. apply sym_equal. exact zenon_H120. % 10.13/10.31 apply zenon_H14d. apply refl_equal. % 10.13/10.31 apply zenon_H14d. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L93_ *) % 10.13/10.31 assert (zenon_L94_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H157 zenon_H158 zenon_H159. % 10.13/10.31 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H157. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H158. % 10.13/10.31 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H15a]. % 10.13/10.31 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H5d. apply refl_equal. % 10.13/10.31 apply zenon_H15a. apply sym_equal. exact zenon_H159. % 10.13/10.31 (* end of lemma zenon_L94_ *) % 10.13/10.31 assert (zenon_L95_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H15b zenon_Hfd zenon_Hb9 zenon_H154 zenon_H127 zenon_H104 zenon_H103 zenon_H157 zenon_H158. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.13/10.31 apply (zenon_L92_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.13/10.31 apply (zenon_L93_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.13/10.31 apply (zenon_L62_); trivial. % 10.13/10.31 apply (zenon_L94_); trivial. % 10.13/10.31 (* end of lemma zenon_L95_ *) % 10.13/10.31 assert (zenon_L96_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H15e zenon_He9 zenon_H1f zenon_H14b zenon_Hcd zenon_H15b zenon_Hfd zenon_Hb9 zenon_H154 zenon_H127 zenon_H104 zenon_H103 zenon_H157. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.31 apply (zenon_L54_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.31 apply (zenon_L90_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.31 apply (zenon_L91_); trivial. % 10.13/10.31 apply (zenon_L95_); trivial. % 10.13/10.31 (* end of lemma zenon_L96_ *) % 10.13/10.31 assert (zenon_L97_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hef zenon_Hdd zenon_Hf4. % 10.13/10.31 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.13/10.31 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hf4. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H86. % 10.13/10.31 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.31 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e1) (e3)) = (e1)) = ((e2) = (e1))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hf5. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hef. % 10.13/10.31 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.31 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hde]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_Hde zenon_Hdd). % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L97_ *) % 10.13/10.31 assert (zenon_L98_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hb6 zenon_H94 zenon_H6b zenon_Hf4 zenon_Hda zenon_Hcd zenon_H12a zenon_Ha3 zenon_Hc6 zenon_He0 zenon_H122 zenon_H124 zenon_Hf6 zenon_H100 zenon_H157 zenon_H104 zenon_H154 zenon_Hb9 zenon_Hfd zenon_H15b zenon_H14b zenon_H1f zenon_He9 zenon_H15e zenon_Hfc zenon_Hbb zenon_Hdf zenon_H99 zenon_Hef. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.31 apply (zenon_L33_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.13/10.31 apply (zenon_L43_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.13/10.31 apply (zenon_L69_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.13/10.31 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.13/10.31 apply (zenon_L76_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.31 apply (zenon_L59_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.31 apply (zenon_L61_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.31 apply (zenon_L96_); trivial. % 10.13/10.31 apply (zenon_L64_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.13/10.31 apply (zenon_L50_); trivial. % 10.13/10.31 apply (zenon_L97_); trivial. % 10.13/10.31 apply (zenon_L71_); trivial. % 10.13/10.31 (* end of lemma zenon_L98_ *) % 10.13/10.31 assert (zenon_L99_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hf6 zenon_H119 zenon_H104. % 10.13/10.31 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.31 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H104. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hea. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e0) (e1)) = (e1)) = ((e3) = (e1))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H105. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hf6. % 10.13/10.31 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.31 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H161 zenon_H119). % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L99_ *) % 10.13/10.31 assert (zenon_L100_ : (~((op (e2) (op (e2) (e2))) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H162 zenon_H103. % 10.13/10.31 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 10.13/10.31 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 exact (zenon_H163 zenon_H103). % 10.13/10.31 (* end of lemma zenon_L100_ *) % 10.13/10.31 assert (zenon_L101_ : ((op (e0) (e2)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e3) = (op (op (e2) (op (e2) (e2))) (e2)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H150 zenon_Hc4 zenon_H103 zenon_H164. % 10.13/10.31 elim (classic ((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 10.13/10.31 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2))) = ((e3) = (op (op (e2) (op (e2) (e2))) (e2)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H164. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H110. % 10.13/10.31 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 10.13/10.31 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e0) (e2)) = (e3)) = ((op (op (e2) (op (e2) (e2))) (e2)) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H165. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H150. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((op (e0) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H166]. % 10.13/10.31 congruence. % 10.13/10.31 elim (classic ((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 10.13/10.31 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2))) = ((op (e0) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H166. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H110. % 10.13/10.31 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 10.13/10.31 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.31 cut (((op (e2) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e2) (e1)) = (e0)) = ((op (e2) (op (e2) (e2))) = (e0))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H168. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hc4. % 10.13/10.31 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.31 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 10.13/10.31 congruence. % 10.13/10.31 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.13/10.31 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e1)) = (op (e2) (op (e2) (e2))))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H169. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H10c. % 10.13/10.31 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.13/10.31 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 10.13/10.31 congruence. % 10.13/10.31 apply (zenon_L100_); trivial. % 10.13/10.31 apply zenon_H10d. apply refl_equal. % 10.13/10.31 apply zenon_H10d. apply refl_equal. % 10.13/10.31 apply zenon_H84. apply refl_equal. % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 apply zenon_H111. apply refl_equal. % 10.13/10.31 apply zenon_H111. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 apply zenon_H111. apply refl_equal. % 10.13/10.31 apply zenon_H111. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L101_ *) % 10.13/10.31 assert (zenon_L102_ : ((op (e0) (e2)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H150 zenon_Hc4 zenon_H103. % 10.13/10.31 apply (zenon_notand_s _ _ ax20); [ zenon_intro zenon_H16b | zenon_intro zenon_H16a ]. % 10.13/10.31 apply zenon_H16b. apply sym_equal. exact zenon_H103. % 10.13/10.31 apply (zenon_notand_s _ _ zenon_H16a); [ zenon_intro zenon_H16c | zenon_intro zenon_H164 ]. % 10.13/10.31 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.13/10.31 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((e0) = (op (e2) (op (e2) (e2))))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H16c. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H10c. % 10.13/10.31 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.13/10.31 cut (((op (e2) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e2) (e1)) = (e0)) = ((op (e2) (op (e2) (e2))) = (e0))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H168. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hc4. % 10.13/10.31 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.31 cut (((op (e2) (e1)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 10.13/10.31 congruence. % 10.13/10.31 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.13/10.31 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e1)) = (op (e2) (op (e2) (e2))))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H169. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H10c. % 10.13/10.31 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.13/10.31 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 10.13/10.31 congruence. % 10.13/10.31 apply (zenon_L100_); trivial. % 10.13/10.31 apply zenon_H10d. apply refl_equal. % 10.13/10.31 apply zenon_H10d. apply refl_equal. % 10.13/10.31 apply zenon_H84. apply refl_equal. % 10.13/10.31 apply zenon_H10d. apply refl_equal. % 10.13/10.31 apply zenon_H10d. apply refl_equal. % 10.13/10.31 apply (zenon_L101_); trivial. % 10.13/10.31 (* end of lemma zenon_L102_ *) % 10.13/10.31 assert (zenon_L103_ : ((op (e0) (e3)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_He5 zenon_H158 zenon_Hfd. % 10.13/10.31 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.31 cut (((e3) = (e3)) = ((e2) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hfd. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hea. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e0) (e3)) = (e2)) = ((e3) = (e2))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hfe. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_He5. % 10.13/10.31 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.31 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H16d zenon_H158). % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L103_ *) % 10.13/10.31 assert (zenon_L104_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H15e zenon_Hef zenon_H99 zenon_H12d zenon_Hb9 zenon_H12a zenon_Hb3 zenon_H6b zenon_H115 zenon_H94 zenon_H1f zenon_Hb6 zenon_Ha3 zenon_Hc6 zenon_Hfc zenon_H104 zenon_H100 zenon_Hf6 zenon_He0 zenon_Hf4 zenon_H122 zenon_H124 zenon_He9 zenon_He5 zenon_Hfd. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.31 apply (zenon_L54_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.31 apply (zenon_L99_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.31 apply (zenon_L33_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.31 apply (zenon_L58_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.31 apply (zenon_L59_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.31 apply (zenon_L61_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.31 apply (zenon_L102_); trivial. % 10.13/10.31 apply (zenon_L64_); trivial. % 10.13/10.31 apply (zenon_L78_); trivial. % 10.13/10.31 apply (zenon_L71_); trivial. % 10.13/10.31 apply (zenon_L103_); trivial. % 10.13/10.31 (* end of lemma zenon_L104_ *) % 10.13/10.31 assert (zenon_L105_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H16e zenon_H150 zenon_H104. % 10.13/10.31 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.31 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H104. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hea. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e0) (e2)) = (e1)) = ((e3) = (e1))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H105. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H16e. % 10.13/10.31 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.31 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H151 zenon_H150). % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L105_ *) % 10.13/10.31 assert (zenon_L106_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H16f zenon_H36 zenon_H115. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hef. zenon_intro zenon_H170. % 10.13/10.31 apply (zenon_L65_); trivial. % 10.13/10.31 (* end of lemma zenon_L106_ *) % 10.13/10.31 assert (zenon_L107_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H171 zenon_H36 zenon_H101. % 10.13/10.31 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H171. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H36. % 10.13/10.31 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 10.13/10.31 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H172. apply refl_equal. % 10.13/10.31 apply zenon_H102. apply sym_equal. exact zenon_H101. % 10.13/10.31 (* end of lemma zenon_L107_ *) % 10.13/10.31 assert (zenon_L108_ : (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H173 zenon_Ha4 zenon_H91. % 10.13/10.31 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H173. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Ha4. % 10.13/10.31 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 10.13/10.31 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H39. apply refl_equal. % 10.13/10.31 apply zenon_H11e. apply sym_equal. exact zenon_H91. % 10.13/10.31 (* end of lemma zenon_L108_ *) % 10.13/10.31 assert (zenon_L109_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hb3 zenon_H6b zenon_H101 zenon_H171 zenon_Ha4 zenon_H173 zenon_Ha3. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.13/10.31 apply (zenon_L107_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.13/10.31 apply (zenon_L108_); trivial. % 10.13/10.31 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.31 (* end of lemma zenon_L109_ *) % 10.13/10.31 assert (zenon_L110_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H131 zenon_H133 zenon_H99. % 10.13/10.31 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H98 ]. % 10.13/10.31 cut (((e1) = (e1)) = ((e0) = (e1))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H99. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hf7. % 10.13/10.31 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.31 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e3) (e0)) = (e0)) = ((e1) = (e0))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hf8. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H131. % 10.13/10.31 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.31 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H174 zenon_H133). % 10.13/10.31 apply zenon_H84. apply refl_equal. % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L110_ *) % 10.13/10.31 assert (zenon_L111_ : ((op (e3) (e1)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H128 zenon_H175 zenon_H99. % 10.13/10.31 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H98 ]. % 10.13/10.31 cut (((e1) = (e1)) = ((e0) = (e1))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H99. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hf7. % 10.13/10.31 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.31 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e3) (e1)) = (e0)) = ((e1) = (e0))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hf8. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H128. % 10.13/10.31 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.31 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H176 zenon_H175). % 10.13/10.31 apply zenon_H84. apply refl_equal. % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L111_ *) % 10.13/10.31 assert (zenon_L112_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> ((op (e2) (e0)) = (e2)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H70 zenon_Hb9. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H6a. zenon_intro zenon_H72. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H6b. zenon_intro zenon_H27. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.13/10.31 exact (zenon_H73 zenon_Hb9). % 10.13/10.31 (* end of lemma zenon_L112_ *) % 10.13/10.31 assert (zenon_L113_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H75 zenon_H13b. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H6a. zenon_intro zenon_H77. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H6b. zenon_intro zenon_H2a. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.13/10.31 exact (zenon_H78 zenon_H13b). % 10.13/10.31 (* end of lemma zenon_L113_ *) % 10.13/10.31 assert (zenon_L114_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H89 zenon_Hb9 zenon_Hc0. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8c. zenon_intro zenon_H43. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.13/10.31 apply (zenon_L88_); trivial. % 10.13/10.31 (* end of lemma zenon_L114_ *) % 10.13/10.31 assert (zenon_L115_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H94 zenon_H31 zenon_H6a. % 10.13/10.31 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H94. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H31. % 10.13/10.31 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 10.13/10.31 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H97. apply refl_equal. % 10.13/10.31 apply zenon_H13a. apply sym_equal. exact zenon_H6a. % 10.13/10.31 (* end of lemma zenon_L115_ *) % 10.13/10.31 assert (zenon_L116_ : ((op (e1) (e1)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Ha2 zenon_H13c zenon_H177. % 10.13/10.31 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H178 | zenon_intro zenon_H172 ]. % 10.13/10.31 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H177. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H178. % 10.13/10.31 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 10.13/10.31 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e1) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H179. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Ha2. % 10.13/10.31 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 10.13/10.31 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H172. apply refl_equal. % 10.13/10.31 apply zenon_H141. apply sym_equal. exact zenon_H13c. % 10.13/10.31 apply zenon_H172. apply refl_equal. % 10.13/10.31 apply zenon_H172. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L116_ *) % 10.13/10.31 assert (zenon_L117_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H142 zenon_H1f zenon_H31 zenon_H94 zenon_Hbb zenon_Hb9 zenon_Ha2 zenon_H177. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H95 | zenon_intro zenon_H143 ]. % 10.13/10.31 apply (zenon_L33_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H6a | zenon_intro zenon_H144 ]. % 10.13/10.31 apply (zenon_L115_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hba | zenon_intro zenon_H13c ]. % 10.13/10.31 apply (zenon_L43_); trivial. % 10.13/10.31 apply (zenon_L116_); trivial. % 10.13/10.31 (* end of lemma zenon_L117_ *) % 10.13/10.31 assert (zenon_L118_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H8b zenon_H17a zenon_H104. % 10.13/10.31 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.31 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H104. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hea. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e1) (e2)) = (e1)) = ((e3) = (e1))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H105. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H8b. % 10.13/10.31 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.31 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H17b zenon_H17a). % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L118_ *) % 10.13/10.31 assert (zenon_L119_ : ((op (e1) (e3)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Ha5 zenon_H17c zenon_He9. % 10.13/10.31 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.31 cut (((e3) = (e3)) = ((e0) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_He9. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hea. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e1) (e3)) = (e0)) = ((e3) = (e0))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hec. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Ha5. % 10.13/10.31 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.31 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H17d zenon_H17c). % 10.13/10.31 apply zenon_H84. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L119_ *) % 10.13/10.31 assert (zenon_L120_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H17e zenon_H13d zenon_H13b zenon_H177 zenon_Hb9 zenon_Hbb zenon_H94 zenon_H31 zenon_H1f zenon_H142 zenon_H104 zenon_H8b zenon_Ha5 zenon_He9. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.31 apply (zenon_L85_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.31 apply (zenon_L117_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.31 apply (zenon_L118_); trivial. % 10.13/10.31 apply (zenon_L119_); trivial. % 10.13/10.31 (* end of lemma zenon_L120_ *) % 10.13/10.31 assert (zenon_L121_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hc0 zenon_H31 zenon_Hfa. % 10.13/10.31 cut (((op (e0) (e0)) = (e1)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hc0. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H31. % 10.13/10.31 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 10.13/10.31 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H97. apply refl_equal. % 10.13/10.31 apply zenon_H181. apply sym_equal. exact zenon_Hfa. % 10.13/10.31 (* end of lemma zenon_L121_ *) % 10.13/10.31 assert (zenon_L122_ : ((op (e2) (e2)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H103 zenon_H8b zenon_H182. % 10.13/10.31 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd0 ]. % 10.13/10.31 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H182. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hcf. % 10.13/10.31 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.31 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H183. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H103. % 10.13/10.31 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 10.13/10.31 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_Hd0. apply refl_equal. % 10.13/10.31 apply zenon_H184. apply sym_equal. exact zenon_H8b. % 10.13/10.31 apply zenon_Hd0. apply refl_equal. % 10.13/10.31 apply zenon_Hd0. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L122_ *) % 10.13/10.31 assert (zenon_L123_ : (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H104 zenon_H13b zenon_H133. % 10.13/10.31 cut (((op (e3) (e0)) = (e3)) = ((e1) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H104. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H13b. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H174 zenon_H133). % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L123_ *) % 10.13/10.31 assert (zenon_L124_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H14b zenon_Hf6 zenon_H175. % 10.13/10.31 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H14b. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hf6. % 10.13/10.31 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 10.13/10.31 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H39. apply refl_equal. % 10.13/10.31 apply zenon_H185. apply sym_equal. exact zenon_H175. % 10.13/10.31 (* end of lemma zenon_L124_ *) % 10.13/10.31 assert (zenon_L125_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H186 zenon_H8b zenon_H187. % 10.13/10.31 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H186. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H8b. % 10.13/10.31 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 10.13/10.31 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H9e. apply refl_equal. % 10.13/10.31 apply zenon_H188. apply sym_equal. exact zenon_H187. % 10.13/10.31 (* end of lemma zenon_L125_ *) % 10.13/10.31 assert (zenon_L126_ : ((op (e3) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H189 zenon_H107 zenon_Hd5. % 10.13/10.31 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.13/10.31 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hd5. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hd6. % 10.13/10.31 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.31 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hd8. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H189. % 10.13/10.31 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 10.13/10.31 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_Hd7. apply refl_equal. % 10.13/10.31 apply zenon_H123. apply sym_equal. exact zenon_H107. % 10.13/10.31 apply zenon_Hd7. apply refl_equal. % 10.13/10.31 apply zenon_Hd7. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L126_ *) % 10.13/10.31 assert (zenon_L127_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H18a zenon_H13b zenon_H104 zenon_Hf6 zenon_H14b zenon_H8b zenon_H186 zenon_H107 zenon_Hd5. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.13/10.31 apply (zenon_L123_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.13/10.31 apply (zenon_L124_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.13/10.31 apply (zenon_L125_); trivial. % 10.13/10.31 apply (zenon_L126_); trivial. % 10.13/10.31 (* end of lemma zenon_L127_ *) % 10.13/10.31 assert (zenon_L128_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H8b zenon_H6a zenon_H18d. % 10.13/10.31 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H9d | zenon_intro zenon_H9e ]. % 10.13/10.31 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e1) (e0)) = (op (e1) (e2)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H18d. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H9d. % 10.13/10.31 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 10.13/10.31 cut (((op (e1) (e2)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18e]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H18e. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H8b. % 10.13/10.31 cut (((e1) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13a]. % 10.13/10.31 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H9e. apply refl_equal. % 10.13/10.31 apply zenon_H13a. apply sym_equal. exact zenon_H6a. % 10.13/10.31 apply zenon_H9e. apply refl_equal. % 10.13/10.31 apply zenon_H9e. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L128_ *) % 10.13/10.31 assert (zenon_L129_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H18f zenon_H6a zenon_H18d. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H8b. zenon_intro zenon_H190. % 10.13/10.31 apply (zenon_L128_); trivial. % 10.13/10.31 (* end of lemma zenon_L129_ *) % 10.13/10.31 assert (zenon_L130_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H191 zenon_Hd5 zenon_H186 zenon_H8b zenon_H14b zenon_Hf6 zenon_H18a zenon_H182 zenon_H100 zenon_Hc0 zenon_H124 zenon_H18d zenon_H18f zenon_Hb9 zenon_Hf4 zenon_H104 zenon_H13b. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.31 apply (zenon_L121_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.31 apply (zenon_L61_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.31 apply (zenon_L122_); trivial. % 10.13/10.31 apply (zenon_L127_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.13/10.31 apply (zenon_L129_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.13/10.31 apply (zenon_L59_); trivial. % 10.13/10.31 apply (zenon_L123_); trivial. % 10.13/10.31 (* end of lemma zenon_L130_ *) % 10.13/10.31 assert (zenon_L131_ : ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H8b zenon_H16e zenon_Hda. % 10.13/10.31 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H9d | zenon_intro zenon_H9e ]. % 10.13/10.31 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hda. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H9d. % 10.13/10.31 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 10.13/10.31 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H194. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H8b. % 10.13/10.31 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 10.13/10.31 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H9e. apply refl_equal. % 10.13/10.31 apply zenon_H195. apply sym_equal. exact zenon_H16e. % 10.13/10.31 apply zenon_H9e. apply refl_equal. % 10.13/10.31 apply zenon_H9e. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L131_ *) % 10.13/10.31 assert (zenon_L132_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hb6 zenon_H1f zenon_H94 zenon_H6b zenon_H99 zenon_H17e zenon_H13d zenon_H13b zenon_Ha4 zenon_H104 zenon_H8b zenon_He9. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.31 apply (zenon_L33_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.31 apply (zenon_L35_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.31 apply (zenon_L85_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.31 apply (zenon_L40_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.31 apply (zenon_L118_); trivial. % 10.13/10.31 apply (zenon_L119_); trivial. % 10.13/10.31 (* end of lemma zenon_L132_ *) % 10.13/10.31 assert (zenon_L133_ : ((op (e3) (e0)) = (e3)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H13b zenon_H5a zenon_H130. % 10.13/10.31 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 10.13/10.31 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e0) (e0)) = (op (e3) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H130. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H13e. % 10.13/10.31 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 10.13/10.31 cut (((op (e3) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e0) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H196. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H13b. % 10.13/10.31 cut (((e3) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 10.13/10.31 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H13f. apply refl_equal. % 10.13/10.31 apply zenon_H197. apply sym_equal. exact zenon_H5a. % 10.13/10.31 apply zenon_H13f. apply refl_equal. % 10.13/10.31 apply zenon_H13f. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L133_ *) % 10.13/10.31 assert (zenon_L134_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H2d zenon_H119 zenon_He9. % 10.13/10.31 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.31 cut (((e3) = (e3)) = ((e0) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_He9. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hea. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e0) (e1)) = (e0)) = ((e3) = (e0))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hec. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H2d. % 10.13/10.31 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.31 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H161 zenon_H119). % 10.13/10.31 apply zenon_H84. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L134_ *) % 10.13/10.31 assert (zenon_L135_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H198 zenon_H158 zenon_H104. % 10.13/10.31 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.31 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H104. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hea. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e0) (e3)) = (e1)) = ((e3) = (e1))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H105. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H198. % 10.13/10.31 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.31 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H16d zenon_H158). % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L135_ *) % 10.13/10.31 assert (zenon_L136_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H15e zenon_H130 zenon_H13b zenon_He9 zenon_H2d zenon_Hfd zenon_Hcd zenon_H198 zenon_H104. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.31 apply (zenon_L133_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.31 apply (zenon_L134_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.31 apply (zenon_L91_); trivial. % 10.13/10.31 apply (zenon_L135_); trivial. % 10.13/10.31 (* end of lemma zenon_L136_ *) % 10.13/10.31 assert (zenon_L137_ : ((op (e2) (e1)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hc4 zenon_Hdd zenon_Ha2. % 10.13/10.31 apply (zenon_notand_s _ _ ax17); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H199 ]. % 10.13/10.31 apply zenon_Hb1. apply sym_equal. exact zenon_Ha2. % 10.13/10.31 apply (zenon_notand_s _ _ zenon_H199); [ zenon_intro zenon_H19b | zenon_intro zenon_H19a ]. % 10.13/10.31 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.31 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((e2) = (op (e1) (op (e1) (e1))))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H19b. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hae. % 10.13/10.31 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.31 cut (((op (e1) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e1) (e3)) = (e2)) = ((op (e1) (op (e1) (e1))) = (e2))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H19c. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hdd. % 10.13/10.31 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.31 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 10.13/10.31 congruence. % 10.13/10.31 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.31 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e3)) = (op (e1) (op (e1) (e1))))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Had. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hae. % 10.13/10.31 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.31 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 10.13/10.31 congruence. % 10.13/10.31 apply (zenon_L37_); trivial. % 10.13/10.31 apply zenon_Haf. apply refl_equal. % 10.13/10.31 apply zenon_Haf. apply refl_equal. % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 apply zenon_Haf. apply refl_equal. % 10.13/10.31 apply zenon_Haf. apply refl_equal. % 10.13/10.31 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.13/10.31 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((e0) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H19a. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Ha7. % 10.13/10.31 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.13/10.31 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H19d]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e2) (e1)) = (e0)) = ((op (op (e1) (op (e1) (e1))) (e1)) = (e0))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H19d. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hc4. % 10.13/10.31 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.31 cut (((op (e2) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 10.13/10.31 congruence. % 10.13/10.31 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.13/10.31 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((op (e2) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H19e. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Ha7. % 10.13/10.31 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.13/10.31 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.31 cut (((op (e1) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e1) (e3)) = (e2)) = ((op (e1) (op (e1) (e1))) = (e2))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H19c. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hdd. % 10.13/10.31 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.31 cut (((op (e1) (e3)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 10.13/10.31 congruence. % 10.13/10.31 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.31 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e3)) = (op (e1) (op (e1) (e1))))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Had. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hae. % 10.13/10.31 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.31 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 10.13/10.31 congruence. % 10.13/10.31 apply (zenon_L37_); trivial. % 10.13/10.31 apply zenon_Haf. apply refl_equal. % 10.13/10.31 apply zenon_Haf. apply refl_equal. % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 apply zenon_Ha8. apply refl_equal. % 10.13/10.31 apply zenon_Ha8. apply refl_equal. % 10.13/10.31 apply zenon_H84. apply refl_equal. % 10.13/10.31 apply zenon_Ha8. apply refl_equal. % 10.13/10.31 apply zenon_Ha8. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L137_ *) % 10.13/10.31 assert (zenon_L138_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H17e zenon_H13d zenon_H13b zenon_Hdd zenon_Hc4 zenon_H104 zenon_H8b zenon_Ha5 zenon_He9. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.31 apply (zenon_L85_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.31 apply (zenon_L137_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.31 apply (zenon_L118_); trivial. % 10.13/10.31 apply (zenon_L119_); trivial. % 10.13/10.31 (* end of lemma zenon_L138_ *) % 10.13/10.31 assert (zenon_L139_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hdf zenon_Hbb zenon_Hb9 zenon_H8c zenon_Hcd zenon_Hda zenon_H17e zenon_H13d zenon_H13b zenon_Hc4 zenon_H104 zenon_H8b zenon_Ha5 zenon_He9. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.13/10.31 apply (zenon_L43_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.13/10.31 exact (zenon_H8c zenon_H91). % 10.13/10.31 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.13/10.31 apply (zenon_L50_); trivial. % 10.13/10.31 apply (zenon_L138_); trivial. % 10.13/10.31 (* end of lemma zenon_L139_ *) % 10.13/10.31 assert (zenon_L140_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_He6 zenon_H198 zenon_H189. % 10.13/10.31 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_He6. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H198. % 10.13/10.31 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 10.13/10.31 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H5d. apply refl_equal. % 10.13/10.31 apply zenon_H1a0. apply sym_equal. exact zenon_H189. % 10.13/10.31 (* end of lemma zenon_L140_ *) % 10.13/10.31 assert (zenon_L141_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H18a zenon_H31 zenon_H130 zenon_H99 zenon_H128 zenon_H8b zenon_H186 zenon_He6 zenon_H198. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.13/10.31 apply (zenon_L82_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.13/10.31 apply (zenon_L111_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.13/10.31 apply (zenon_L125_); trivial. % 10.13/10.31 apply (zenon_L140_); trivial. % 10.13/10.31 (* end of lemma zenon_L141_ *) % 10.13/10.31 assert (zenon_L142_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hb6 zenon_H1f zenon_H94 zenon_H12d zenon_Hfd zenon_H15e zenon_H6b zenon_He9 zenon_H104 zenon_H13b zenon_H13d zenon_H17e zenon_Hda zenon_Hcd zenon_H8c zenon_Hb9 zenon_Hbb zenon_Hdf zenon_H18a zenon_H31 zenon_H130 zenon_H99 zenon_H8b zenon_H186 zenon_He6 zenon_H198. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.31 apply (zenon_L33_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.31 apply (zenon_L35_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.31 apply (zenon_L136_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.31 apply (zenon_L139_); trivial. % 10.13/10.31 apply (zenon_L141_); trivial. % 10.13/10.31 (* end of lemma zenon_L142_ *) % 10.13/10.31 assert (zenon_L143_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H198 zenon_He5 zenon_Hf4. % 10.13/10.31 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.13/10.31 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hf4. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H86. % 10.13/10.31 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.31 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e0) (e3)) = (e1)) = ((e2) = (e1))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_Hf5. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H198. % 10.13/10.31 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.31 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H1a1 zenon_He5). % 10.13/10.31 apply zenon_H98. apply refl_equal. % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 apply zenon_H87. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L143_ *) % 10.13/10.31 assert (zenon_L144_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1a2 zenon_H142 zenon_H177 zenon_H18f zenon_H124 zenon_Hc0 zenon_H100 zenon_H182 zenon_H14b zenon_Hd5 zenon_H191 zenon_Hb6 zenon_H1f zenon_H94 zenon_H12d zenon_Hfd zenon_H15e zenon_H6b zenon_He9 zenon_H13d zenon_H17e zenon_Hda zenon_H8c zenon_Hbb zenon_Hdf zenon_H18a zenon_H130 zenon_H99 zenon_H186 zenon_He6 zenon_H1a3 zenon_H18d zenon_H8b zenon_Hb9 zenon_Hf4 zenon_H104 zenon_H13b. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.31 apply (zenon_L33_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.31 apply (zenon_L35_); trivial. % 10.13/10.31 apply (zenon_L120_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.13/10.31 apply (zenon_L130_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.13/10.31 apply (zenon_L131_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.13/10.31 apply (zenon_L57_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.13/10.31 apply (zenon_L132_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.13/10.31 apply (zenon_L142_); trivial. % 10.13/10.31 apply (zenon_L143_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.13/10.31 apply (zenon_L128_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.13/10.31 apply (zenon_L59_); trivial. % 10.13/10.31 apply (zenon_L123_); trivial. % 10.13/10.31 (* end of lemma zenon_L144_ *) % 10.13/10.31 assert (zenon_L145_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hed zenon_H13b zenon_H130. % 10.13/10.31 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hef. zenon_intro zenon_Hee. % 10.13/10.31 apply (zenon_and_s _ _ zenon_Hee). zenon_intro zenon_Ha3. zenon_intro zenon_H57. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.13/10.31 apply (zenon_L133_); trivial. % 10.13/10.31 (* end of lemma zenon_L145_ *) % 10.13/10.31 assert (zenon_L146_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H16f zenon_H142 zenon_H1f zenon_H94 zenon_H138 zenon_Hbb zenon_Hb9 zenon_H13b zenon_H13d. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hef. zenon_intro zenon_H170. % 10.13/10.31 apply (zenon_L86_); trivial. % 10.13/10.31 (* end of lemma zenon_L146_ *) % 10.13/10.31 assert (zenon_L147_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1a8. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hef. zenon_intro zenon_H1a9. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_Ha3. zenon_intro zenon_H65. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 10.13/10.31 exact (zenon_H66 zenon_H67). % 10.13/10.31 (* end of lemma zenon_L147_ *) % 10.13/10.31 assert (zenon_L148_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1aa. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_Hb9. zenon_intro zenon_H1ab. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1ab). zenon_intro zenon_H71. zenon_intro zenon_H20. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H1f. zenon_intro zenon_H21. % 10.13/10.31 exact (zenon_H21 zenon_H1f). % 10.13/10.31 (* end of lemma zenon_L148_ *) % 10.13/10.31 assert (zenon_L149_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> (~((op (e1) (e1)) = (e0))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1ac zenon_H6b. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_Hb9. zenon_intro zenon_H1ad. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H71. zenon_intro zenon_H24. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 (* end of lemma zenon_L149_ *) % 10.13/10.31 assert (zenon_L150_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1ae. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_Hb9. zenon_intro zenon_H1af. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1af). zenon_intro zenon_H71. zenon_intro zenon_H27. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.13/10.31 exact (zenon_H73 zenon_Hb9). % 10.13/10.31 (* end of lemma zenon_L150_ *) % 10.13/10.31 assert (zenon_L151_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1b0 zenon_H13b. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb9. zenon_intro zenon_H1b1. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H71. zenon_intro zenon_H2a. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.13/10.31 exact (zenon_H78 zenon_H13b). % 10.13/10.31 (* end of lemma zenon_L151_ *) % 10.13/10.31 assert (zenon_L152_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hc3 zenon_Hb9 zenon_H1b2. % 10.13/10.31 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H1b4 ]. % 10.13/10.31 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e2) (e0)) = (op (e2) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H1b2. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H1b3. % 10.13/10.31 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 10.13/10.31 cut (((op (e2) (e1)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H1b5. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hc3. % 10.13/10.31 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 10.13/10.31 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H1b4. apply refl_equal. % 10.13/10.31 apply zenon_H1b6. apply sym_equal. exact zenon_Hb9. % 10.13/10.31 apply zenon_H1b4. apply refl_equal. % 10.13/10.31 apply zenon_H1b4. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L152_ *) % 10.13/10.31 assert (zenon_L153_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1b7 zenon_Hb9 zenon_H1b2. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.13/10.31 apply (zenon_L152_); trivial. % 10.13/10.31 (* end of lemma zenon_L153_ *) % 10.13/10.31 assert (zenon_L154_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1b9. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1b9). zenon_intro zenon_Hc3. zenon_intro zenon_H1ba. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1ba). zenon_intro zenon_H163. zenon_intro zenon_H34. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 10.13/10.31 exact (zenon_H35 zenon_H36). % 10.13/10.31 (* end of lemma zenon_L154_ *) % 10.13/10.31 assert (zenon_L155_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1bb. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_Hc3. zenon_intro zenon_H1bc. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1bc). zenon_intro zenon_H163. zenon_intro zenon_H80. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.13/10.31 exact (zenon_H1bd zenon_Hc3). % 10.13/10.31 (* end of lemma zenon_L155_ *) % 10.13/10.31 assert (zenon_L156_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1be zenon_Hb9 zenon_H1b2. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_Hc3. zenon_intro zenon_H1bf. % 10.13/10.31 apply (zenon_L152_); trivial. % 10.13/10.31 (* end of lemma zenon_L156_ *) % 10.13/10.31 assert (zenon_L157_ : (((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1c0. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H51. zenon_intro zenon_H1c1. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1c1). zenon_intro zenon_H50. zenon_intro zenon_H43. % 10.13/10.31 exact (zenon_H50 zenon_H51). % 10.13/10.31 (* end of lemma zenon_L157_ *) % 10.13/10.31 assert (zenon_L158_ : (((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1c2. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1c2). zenon_intro zenon_H51. zenon_intro zenon_H1c3. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H50. zenon_intro zenon_H8f. % 10.13/10.31 exact (zenon_H50 zenon_H51). % 10.13/10.31 (* end of lemma zenon_L158_ *) % 10.13/10.31 assert (zenon_L159_ : (((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1c4. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1c4). zenon_intro zenon_H51. zenon_intro zenon_H1c5. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1c5). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H50. % 10.13/10.31 exact (zenon_H50 zenon_H51). % 10.13/10.31 (* end of lemma zenon_L159_ *) % 10.13/10.31 assert (zenon_L160_ : (((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1c6. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1c6). zenon_intro zenon_H51. zenon_intro zenon_H1c7. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_H50. zenon_intro zenon_H1c8. % 10.13/10.31 exact (zenon_H50 zenon_H51). % 10.13/10.31 (* end of lemma zenon_L160_ *) % 10.13/10.31 assert (zenon_L161_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1c9 zenon_H13b zenon_H130. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_Hd4. zenon_intro zenon_H1ca. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1ca). zenon_intro zenon_Hff. zenon_intro zenon_H57. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.13/10.31 apply (zenon_L133_); trivial. % 10.13/10.31 (* end of lemma zenon_L161_ *) % 10.13/10.31 assert (zenon_L162_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_Hd4 zenon_Hb9 zenon_H1cb. % 10.13/10.31 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cd ]. % 10.13/10.31 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e0)) = (op (e2) (e3)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H1cb. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H1cc. % 10.13/10.31 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 10.13/10.31 cut (((op (e2) (e3)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H1ce. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hd4. % 10.13/10.31 cut (((e2) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 10.13/10.31 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H1cd. apply refl_equal. % 10.13/10.31 apply zenon_H1b6. apply sym_equal. exact zenon_Hb9. % 10.13/10.31 apply zenon_H1cd. apply refl_equal. % 10.13/10.31 apply zenon_H1cd. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L162_ *) % 10.13/10.31 assert (zenon_L163_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1cf zenon_Hb9 zenon_H1cb. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_Hd4. zenon_intro zenon_H1d0. % 10.13/10.31 apply (zenon_L162_); trivial. % 10.13/10.31 (* end of lemma zenon_L163_ *) % 10.13/10.31 assert (zenon_L164_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1d1. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_Hd4. zenon_intro zenon_H1d2. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1d2). zenon_intro zenon_Hff. zenon_intro zenon_H1d3. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.13/10.31 exact (zenon_Hff zenon_Hfc). % 10.13/10.31 (* end of lemma zenon_L164_ *) % 10.13/10.31 assert (zenon_L165_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1d4. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_Hd4. zenon_intro zenon_H1d5. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_Hff. zenon_intro zenon_H65. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 10.13/10.31 exact (zenon_H66 zenon_H67). % 10.13/10.31 (* end of lemma zenon_L165_ *) % 10.13/10.31 assert (zenon_L166_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1d6. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H13b. zenon_intro zenon_H1d7. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H76. zenon_intro zenon_H20. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H1f. zenon_intro zenon_H21. % 10.13/10.31 exact (zenon_H21 zenon_H1f). % 10.13/10.31 (* end of lemma zenon_L166_ *) % 10.13/10.31 assert (zenon_L167_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> (~((op (e1) (e1)) = (e0))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1d8 zenon_H6b. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1d8). zenon_intro zenon_H13b. zenon_intro zenon_H1d9. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1d9). zenon_intro zenon_H76. zenon_intro zenon_H24. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.13/10.31 exact (zenon_H6b zenon_H6f). % 10.13/10.31 (* end of lemma zenon_L167_ *) % 10.13/10.31 assert (zenon_L168_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> ((op (e2) (e0)) = (e2)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1da zenon_Hb9. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_H13b. zenon_intro zenon_H1db. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1db). zenon_intro zenon_H76. zenon_intro zenon_H27. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.13/10.31 exact (zenon_H73 zenon_Hb9). % 10.13/10.31 (* end of lemma zenon_L168_ *) % 10.13/10.31 assert (zenon_L169_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1dc. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1dc). zenon_intro zenon_H13b. zenon_intro zenon_H1dd. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1dd). zenon_intro zenon_H76. zenon_intro zenon_H2a. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.13/10.31 exact (zenon_H78 zenon_H13b). % 10.13/10.31 (* end of lemma zenon_L169_ *) % 10.13/10.31 assert (zenon_L170_ : ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H127 zenon_H13b zenon_H1de. % 10.13/10.31 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H14c | zenon_intro zenon_H14d ]. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (e0)) = (op (e3) (e1)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H1de. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H14c. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H1df. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H127. % 10.13/10.31 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 10.13/10.31 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H14d. apply refl_equal. % 10.13/10.31 apply zenon_H1e0. apply sym_equal. exact zenon_H13b. % 10.13/10.31 apply zenon_H14d. apply refl_equal. % 10.13/10.31 apply zenon_H14d. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L170_ *) % 10.13/10.31 assert (zenon_L171_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1e1 zenon_H13b zenon_H1de. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H127. zenon_intro zenon_H1e2. % 10.13/10.31 apply (zenon_L170_); trivial. % 10.13/10.31 (* end of lemma zenon_L171_ *) % 10.13/10.31 assert (zenon_L172_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1e3. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1e3). zenon_intro zenon_H127. zenon_intro zenon_H1e4. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1e4). zenon_intro zenon_H1e5. zenon_intro zenon_H34. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35. % 10.13/10.31 exact (zenon_H35 zenon_H36). % 10.13/10.31 (* end of lemma zenon_L172_ *) % 10.13/10.31 assert (zenon_L173_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1e6 zenon_H13b zenon_H1de. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H127. zenon_intro zenon_H1e7. % 10.13/10.31 apply (zenon_L170_); trivial. % 10.13/10.31 (* end of lemma zenon_L173_ *) % 10.13/10.31 assert (zenon_L174_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1e8. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1e8). zenon_intro zenon_H127. zenon_intro zenon_H1e9. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_H1e5. zenon_intro zenon_H83. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.13/10.31 exact (zenon_H1ea zenon_H127). % 10.13/10.31 (* end of lemma zenon_L174_ *) % 10.13/10.31 assert (zenon_L175_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1eb zenon_Hb9 zenon_Hc0. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ed. zenon_intro zenon_H1ec. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ee. zenon_intro zenon_H43. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.13/10.31 apply (zenon_L88_); trivial. % 10.13/10.31 (* end of lemma zenon_L175_ *) % 10.13/10.31 assert (zenon_L176_ : ((op (e3) (e2)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1ed zenon_H13b zenon_H1ef. % 10.13/10.31 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ]. % 10.13/10.31 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e0)) = (op (e3) (e2)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H1ef. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H1f0. % 10.13/10.31 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 10.13/10.31 cut (((op (e3) (e2)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e0)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H1f2. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H1ed. % 10.13/10.31 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 10.13/10.31 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_H1f1. apply refl_equal. % 10.13/10.31 apply zenon_H1e0. apply sym_equal. exact zenon_H13b. % 10.13/10.31 apply zenon_H1f1. apply refl_equal. % 10.13/10.31 apply zenon_H1f1. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L176_ *) % 10.13/10.31 assert (zenon_L177_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1f3 zenon_H13b zenon_H1ef. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H1ed. zenon_intro zenon_H1f4. % 10.13/10.31 apply (zenon_L176_); trivial. % 10.13/10.31 (* end of lemma zenon_L177_ *) % 10.13/10.31 assert (zenon_L178_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1f5. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1f5). zenon_intro zenon_H1ed. zenon_intro zenon_H1f6. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1f6). zenon_intro zenon_H1ee. zenon_intro zenon_H4f. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H50. % 10.13/10.31 exact (zenon_H50 zenon_H51). % 10.13/10.31 (* end of lemma zenon_L178_ *) % 10.13/10.31 assert (zenon_L179_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1f7. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1f7). zenon_intro zenon_H1ed. zenon_intro zenon_H1f8. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1f8). zenon_intro zenon_H1ee. zenon_intro zenon_H1c8. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.13/10.31 exact (zenon_H1f9 zenon_H1ed). % 10.13/10.31 (* end of lemma zenon_L179_ *) % 10.13/10.31 assert (zenon_L180_ : (((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1fa. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_H67. zenon_intro zenon_H1fb. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H66. zenon_intro zenon_H57. % 10.13/10.31 exact (zenon_H66 zenon_H67). % 10.13/10.31 (* end of lemma zenon_L180_ *) % 10.13/10.31 assert (zenon_L181_ : (((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1fc. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H67. zenon_intro zenon_H1fd. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H66. zenon_intro zenon_Hf2. % 10.13/10.31 exact (zenon_H66 zenon_H67). % 10.13/10.31 (* end of lemma zenon_L181_ *) % 10.13/10.31 assert (zenon_L182_ : (((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H1fe. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H67. zenon_intro zenon_H1ff. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H1ff). zenon_intro zenon_H66. zenon_intro zenon_H1d3. % 10.13/10.31 exact (zenon_H66 zenon_H67). % 10.13/10.31 (* end of lemma zenon_L182_ *) % 10.13/10.31 assert (zenon_L183_ : (((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H200. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H200). zenon_intro zenon_H67. zenon_intro zenon_H201. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H201). zenon_intro zenon_H66. zenon_intro zenon_H65. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 10.13/10.31 exact (zenon_H66 zenon_H67). % 10.13/10.31 (* end of lemma zenon_L183_ *) % 10.13/10.31 assert (zenon_L184_ : ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H104 zenon_Hf4 zenon_H18d zenon_H1a3 zenon_He6 zenon_H186 zenon_H99 zenon_H18a zenon_Hdf zenon_Hda zenon_H17e zenon_He9 zenon_H15e zenon_Hfd zenon_H12d zenon_Hb6 zenon_H191 zenon_Hd5 zenon_H14b zenon_H182 zenon_H100 zenon_H124 zenon_H177 zenon_H1a2 zenon_H13d zenon_Hbb zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6b zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef zenon_H13b. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.13/10.31 apply (zenon_L1_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.13/10.31 apply (zenon_L2_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.13/10.31 apply (zenon_L3_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.13/10.31 apply (zenon_L4_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.13/10.31 apply (zenon_L5_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.13/10.31 apply (zenon_L6_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.13/10.31 apply (zenon_L8_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.13/10.31 apply (zenon_L9_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.13/10.31 apply (zenon_L10_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.13/10.31 apply (zenon_L12_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.13/10.31 apply (zenon_L13_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.13/10.31 apply (zenon_L14_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.13/10.31 apply (zenon_L15_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.13/10.31 apply (zenon_L17_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.13/10.31 apply (zenon_L18_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.13/10.31 apply (zenon_L19_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.13/10.31 apply (zenon_L20_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.13/10.31 apply (zenon_L21_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.13/10.31 apply (zenon_L112_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.13/10.31 apply (zenon_L113_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.13/10.31 apply (zenon_L24_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.13/10.31 apply (zenon_L25_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.13/10.31 apply (zenon_L26_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.13/10.31 apply (zenon_L27_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.13/10.31 apply (zenon_L114_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.13/10.31 apply (zenon_L31_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.13/10.31 apply (zenon_L32_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H8b. zenon_intro zenon_H190. % 10.13/10.31 apply (zenon_and_s _ _ zenon_H190). zenon_intro zenon_H8c. zenon_intro zenon_H1c8. % 10.13/10.31 apply (zenon_L144_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.13/10.31 apply (zenon_L145_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.13/10.31 apply (zenon_L56_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.13/10.31 apply (zenon_L146_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.13/10.31 apply (zenon_L147_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.13/10.31 apply (zenon_L148_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.13/10.31 apply (zenon_L149_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.13/10.31 apply (zenon_L150_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.13/10.31 apply (zenon_L151_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.13/10.31 apply (zenon_L153_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.13/10.31 apply (zenon_L154_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.13/10.31 apply (zenon_L155_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.13/10.31 apply (zenon_L156_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.13/10.31 apply (zenon_L157_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.13/10.31 apply (zenon_L158_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.13/10.31 apply (zenon_L159_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.13/10.31 apply (zenon_L160_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.13/10.31 apply (zenon_L161_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.13/10.31 apply (zenon_L163_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.13/10.31 apply (zenon_L164_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.13/10.31 apply (zenon_L165_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.13/10.31 apply (zenon_L166_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.13/10.31 apply (zenon_L167_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.13/10.31 apply (zenon_L168_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.13/10.31 apply (zenon_L169_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.13/10.31 apply (zenon_L171_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.13/10.31 apply (zenon_L172_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.13/10.31 apply (zenon_L173_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.13/10.31 apply (zenon_L174_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.13/10.31 apply (zenon_L175_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.13/10.31 apply (zenon_L177_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.13/10.31 apply (zenon_L178_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.13/10.31 apply (zenon_L179_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.13/10.31 apply (zenon_L180_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.13/10.31 apply (zenon_L181_); trivial. % 10.13/10.31 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.13/10.31 apply (zenon_L182_); trivial. % 10.13/10.31 apply (zenon_L183_); trivial. % 10.13/10.31 (* end of lemma zenon_L184_ *) % 10.13/10.31 assert (zenon_L185_ : (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> False). % 10.13/10.31 do 0 intro. intros zenon_He9 zenon_H1ed zenon_H241. % 10.13/10.31 cut (((op (e3) (e2)) = (e3)) = ((e0) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_He9. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H1ed. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H242]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H242 zenon_H241). % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L185_ *) % 10.13/10.31 assert (zenon_L186_ : ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.31 do 0 intro. intros zenon_H67 zenon_H158 zenon_He6. % 10.13/10.31 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.13/10.31 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_He6. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_Hd6. % 10.13/10.31 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.31 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 10.13/10.31 congruence. % 10.13/10.31 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_He7. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H67. % 10.13/10.31 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 10.13/10.31 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.31 congruence. % 10.13/10.31 apply zenon_Hd7. apply refl_equal. % 10.13/10.31 apply zenon_H243. apply sym_equal. exact zenon_H158. % 10.13/10.31 apply zenon_Hd7. apply refl_equal. % 10.13/10.31 apply zenon_Hd7. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L186_ *) % 10.13/10.31 assert (zenon_L187_ : (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> False). % 10.13/10.31 do 0 intro. intros zenon_H104 zenon_H127 zenon_H175. % 10.13/10.31 cut (((op (e3) (e1)) = (e3)) = ((e1) = (e3))). % 10.13/10.31 intro zenon_D_pnotp. % 10.13/10.31 apply zenon_H104. % 10.13/10.31 rewrite <- zenon_D_pnotp. % 10.13/10.31 exact zenon_H127. % 10.13/10.31 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.31 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 10.13/10.31 congruence. % 10.13/10.31 exact (zenon_H176 zenon_H175). % 10.13/10.31 apply zenon_Heb. apply refl_equal. % 10.13/10.31 (* end of lemma zenon_L187_ *) % 10.13/10.31 assert (zenon_L188_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((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))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H12a zenon_Hef zenon_Hb3 zenon_H115 zenon_Ha3 zenon_H76 zenon_H244 zenon_H1ef zenon_Hb9 zenon_Hc0 zenon_H1de zenon_H6b zenon_H1cb zenon_H130 zenon_H1b2 zenon_H142 zenon_H1f zenon_H94 zenon_H138 zenon_Hbb zenon_H13d zenon_H1a2 zenon_H177 zenon_H124 zenon_H100 zenon_H182 zenon_H14b zenon_Hd5 zenon_H191 zenon_Hb6 zenon_H12d zenon_Hfd zenon_H15e zenon_H17e zenon_Hda zenon_Hdf zenon_H18a zenon_H99 zenon_H186 zenon_H1a3 zenon_H18d zenon_Hf4 zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_H154 zenon_He9 zenon_H158 zenon_He6 zenon_H133 zenon_H245 zenon_H104 zenon_H175. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.13/10.32 apply (zenon_L72_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.13/10.32 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.13/10.32 apply (zenon_L110_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.13/10.32 apply (zenon_L111_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.13/10.32 apply (zenon_L184_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.13/10.32 apply (zenon_L93_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.13/10.32 apply (zenon_L185_); trivial. % 10.13/10.32 apply (zenon_L186_); trivial. % 10.13/10.32 exact (zenon_H76 zenon_H79). % 10.13/10.32 apply (zenon_L187_); trivial. % 10.13/10.32 (* end of lemma zenon_L188_ *) % 10.13/10.32 assert (zenon_L189_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H16e zenon_Hcd zenon_Hf4. % 10.13/10.32 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.13/10.32 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_Hf4. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H86. % 10.13/10.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.32 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 10.13/10.32 congruence. % 10.13/10.32 cut (((op (e0) (e2)) = (e1)) = ((e2) = (e1))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_Hf5. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H16e. % 10.13/10.32 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.32 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H24a]. % 10.13/10.32 congruence. % 10.13/10.32 exact (zenon_H24a zenon_Hcd). % 10.13/10.32 apply zenon_H98. apply refl_equal. % 10.13/10.32 apply zenon_H87. apply refl_equal. % 10.13/10.32 apply zenon_H87. apply refl_equal. % 10.13/10.32 (* end of lemma zenon_L189_ *) % 10.13/10.32 assert (zenon_L190_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H15e zenon_He9 zenon_Hef zenon_H99 zenon_Hb3 zenon_H6b zenon_H115 zenon_Ha3 zenon_H94 zenon_H1f zenon_Hb6 zenon_H104 zenon_H16e zenon_He5 zenon_Hfd. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.32 apply (zenon_L54_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.32 apply (zenon_L72_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.32 apply (zenon_L105_); trivial. % 10.13/10.32 apply (zenon_L103_); trivial. % 10.13/10.32 (* end of lemma zenon_L190_ *) % 10.13/10.32 assert (zenon_L191_ : ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.13/10.32 do 0 intro. intros zenon_Hef zenon_H198 zenon_H24b. % 10.13/10.32 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H116 | zenon_intro zenon_Hc9 ]. % 10.13/10.32 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H24b. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H116. % 10.13/10.32 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 10.13/10.32 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H24c]. % 10.13/10.32 congruence. % 10.13/10.32 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H24c. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_Hef. % 10.13/10.32 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H24d]. % 10.13/10.32 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 10.13/10.32 congruence. % 10.13/10.32 apply zenon_Hc9. apply refl_equal. % 10.13/10.32 apply zenon_H24d. apply sym_equal. exact zenon_H198. % 10.13/10.32 apply zenon_Hc9. apply refl_equal. % 10.13/10.32 apply zenon_Hc9. apply refl_equal. % 10.13/10.32 (* end of lemma zenon_L191_ *) % 10.13/10.32 assert (zenon_L192_ : (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H122 zenon_He0 zenon_Hfc zenon_Hc6 zenon_H157 zenon_H15b zenon_Hfd zenon_H104 zenon_Hb6 zenon_H1f zenon_H94 zenon_Ha3 zenon_H115 zenon_H6b zenon_Hb3 zenon_H99 zenon_He9 zenon_H15e zenon_Hf4 zenon_H24e zenon_H16f zenon_H173 zenon_H171 zenon_H12a zenon_H76 zenon_H244 zenon_H1ef zenon_Hb9 zenon_Hc0 zenon_H1de zenon_H1cb zenon_H130 zenon_H1b2 zenon_H142 zenon_H138 zenon_Hbb zenon_H13d zenon_H1a2 zenon_H177 zenon_H124 zenon_H100 zenon_H182 zenon_H14b zenon_Hd5 zenon_H191 zenon_H12d zenon_H17e zenon_Hda zenon_Hdf zenon_H18a zenon_H186 zenon_H1a3 zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_H154 zenon_He6 zenon_H245 zenon_H85 zenon_H145 zenon_H135 zenon_Hef zenon_H24b. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.13/10.32 apply (zenon_L87_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.13/10.32 apply (zenon_L88_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.13/10.32 apply (zenon_L89_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.13/10.32 apply (zenon_L98_); trivial. % 10.13/10.32 apply (zenon_L104_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.13/10.32 apply (zenon_L87_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.13/10.32 apply (zenon_L84_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.13/10.32 apply (zenon_L59_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.13/10.32 apply (zenon_L29_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.32 apply (zenon_L54_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.32 apply (zenon_L72_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.32 apply (zenon_L105_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.13/10.32 apply (zenon_L89_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.13/10.32 apply (zenon_L106_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.13/10.32 apply (zenon_L109_); trivial. % 10.13/10.32 apply (zenon_L188_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.13/10.32 apply (zenon_L189_); trivial. % 10.13/10.32 apply (zenon_L190_); trivial. % 10.13/10.32 apply (zenon_L191_); trivial. % 10.13/10.32 (* end of lemma zenon_L192_ *) % 10.13/10.32 assert (zenon_L193_ : (~((e1) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> False). % 10.13/10.32 do 0 intro. intros zenon_Hf4 zenon_Hc3 zenon_H101. % 10.13/10.32 cut (((op (e2) (e1)) = (e2)) = ((e1) = (e2))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_Hf4. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_Hc3. % 10.13/10.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.32 cut (((op (e2) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H251]. % 10.13/10.32 congruence. % 10.13/10.32 exact (zenon_H251 zenon_H101). % 10.13/10.32 apply zenon_H87. apply refl_equal. % 10.13/10.32 (* end of lemma zenon_L193_ *) % 10.13/10.32 assert (zenon_L194_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e3)) = (e2))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H24b zenon_Hef zenon_H135 zenon_H145 zenon_H85 zenon_H245 zenon_He6 zenon_H154 zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H18d zenon_H1a3 zenon_H186 zenon_H18a zenon_Hdf zenon_Hda zenon_H17e zenon_H12d zenon_H191 zenon_Hd5 zenon_H14b zenon_H182 zenon_H100 zenon_H124 zenon_H177 zenon_H1a2 zenon_H13d zenon_Hbb zenon_H138 zenon_H142 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H1de zenon_Hc0 zenon_H1ef zenon_H244 zenon_H76 zenon_H12a zenon_H171 zenon_H173 zenon_H16f zenon_H24e zenon_H15e zenon_He9 zenon_H99 zenon_Hb3 zenon_H6b zenon_H115 zenon_Ha3 zenon_H94 zenon_H1f zenon_Hb6 zenon_H104 zenon_H15b zenon_H157 zenon_Hc6 zenon_He0 zenon_H101 zenon_Hf4 zenon_Hfd zenon_Hfc zenon_H122. % 10.13/10.32 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.32 apply (zenon_L192_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.32 apply (zenon_L193_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.32 apply (zenon_L60_); trivial. % 10.13/10.32 exact (zenon_H122 zenon_Hd4). % 10.13/10.32 (* end of lemma zenon_L194_ *) % 10.13/10.32 assert (zenon_L195_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H12a zenon_H9a zenon_Hef zenon_H115 zenon_H6b zenon_Hb3 zenon_Ha3 zenon_H122 zenon_Hfc zenon_Hfd zenon_Hf4 zenon_Hfa zenon_He0 zenon_H104 zenon_H175. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.13/10.32 apply (zenon_L70_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.13/10.32 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.13/10.32 apply (zenon_L74_); trivial. % 10.13/10.32 apply (zenon_L187_); trivial. % 10.13/10.32 (* end of lemma zenon_L195_ *) % 10.13/10.32 assert (zenon_L196_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H124 zenon_H175 zenon_He0 zenon_Hf4 zenon_Hfd zenon_H122 zenon_H115 zenon_Hef zenon_H12a zenon_Ha3 zenon_H173 zenon_Ha4 zenon_H171 zenon_H6b zenon_Hb3 zenon_H104 zenon_H9a zenon_Hfc. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.32 apply (zenon_L195_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.32 apply (zenon_L109_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.32 apply (zenon_L62_); trivial. % 10.13/10.32 apply (zenon_L64_); trivial. % 10.13/10.32 (* end of lemma zenon_L196_ *) % 10.13/10.32 assert (zenon_L197_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H91 zenon_Hba zenon_H177. % 10.13/10.32 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H178 | zenon_intro zenon_H172 ]. % 10.13/10.32 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e1) (e0)) = (op (e1) (e1)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H177. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H178. % 10.13/10.32 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 10.13/10.32 cut (((op (e1) (e1)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 10.13/10.32 congruence. % 10.13/10.32 cut (((op (e1) (e1)) = (e2)) = ((op (e1) (e1)) = (op (e1) (e0)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H179. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H91. % 10.13/10.32 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 10.13/10.32 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 10.13/10.32 congruence. % 10.13/10.32 apply zenon_H172. apply refl_equal. % 10.13/10.32 apply zenon_Hbf. apply sym_equal. exact zenon_Hba. % 10.13/10.32 apply zenon_H172. apply refl_equal. % 10.13/10.32 apply zenon_H172. apply refl_equal. % 10.13/10.32 (* end of lemma zenon_L197_ *) % 10.13/10.32 assert (zenon_L198_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e2) (e3)) = (e2))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H24b zenon_Hef zenon_H135 zenon_H145 zenon_H85 zenon_H245 zenon_He6 zenon_H154 zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H18d zenon_H1a3 zenon_H186 zenon_H18a zenon_Hdf zenon_Hda zenon_H17e zenon_H12d zenon_H191 zenon_Hd5 zenon_H14b zenon_H182 zenon_H100 zenon_H124 zenon_H177 zenon_H1a2 zenon_H13d zenon_Hbb zenon_H138 zenon_H142 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H1de zenon_Hc0 zenon_H1ef zenon_H244 zenon_H76 zenon_H12a zenon_H171 zenon_H173 zenon_H16f zenon_H24e zenon_Hf4 zenon_H15e zenon_He9 zenon_H99 zenon_Hb3 zenon_H6b zenon_H115 zenon_Ha3 zenon_H94 zenon_H1f zenon_Hb6 zenon_H104 zenon_H15b zenon_H157 zenon_Hc6 zenon_He0 zenon_H120 zenon_Hfd zenon_Hfc zenon_H122. % 10.13/10.32 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.32 apply (zenon_L192_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.32 apply (zenon_L73_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.32 apply (zenon_L60_); trivial. % 10.13/10.32 exact (zenon_H122 zenon_Hd4). % 10.13/10.32 (* end of lemma zenon_L198_ *) % 10.13/10.32 assert (zenon_L199_ : (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> False). % 10.13/10.32 do 0 intro. intros zenon_Hfd zenon_H127 zenon_H252. % 10.13/10.32 cut (((op (e3) (e1)) = (e3)) = ((e2) = (e3))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_Hfd. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H127. % 10.13/10.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.32 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 10.13/10.32 congruence. % 10.13/10.32 exact (zenon_H253 zenon_H252). % 10.13/10.32 apply zenon_Heb. apply refl_equal. % 10.13/10.32 (* end of lemma zenon_L199_ *) % 10.13/10.32 assert (zenon_L200_ : (~((op (e0) (op (e0) (e0))) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e1)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H254 zenon_H31. % 10.13/10.32 cut (((op (e0) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2f]. % 10.13/10.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.32 congruence. % 10.13/10.32 apply zenon_H84. apply refl_equal. % 10.13/10.32 exact (zenon_H2f zenon_H31). % 10.13/10.32 (* end of lemma zenon_L200_ *) % 10.13/10.32 assert (zenon_L201_ : ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((e2) = (op (op (e0) (op (e0) (e0))) (e0)))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H136 zenon_H119 zenon_H31 zenon_H255. % 10.13/10.32 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.13/10.32 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((e2) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H255. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H256. % 10.13/10.32 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.13/10.32 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H258]. % 10.13/10.32 congruence. % 10.13/10.32 cut (((op (e3) (e0)) = (e2)) = ((op (op (e0) (op (e0) (e0))) (e0)) = (e2))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H258. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H136. % 10.13/10.32 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.32 cut (((op (e3) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 10.13/10.32 congruence. % 10.13/10.32 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.13/10.32 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((op (e3) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H259. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H256. % 10.13/10.32 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.13/10.32 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 10.13/10.32 congruence. % 10.13/10.32 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.32 cut (((op (e0) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H25b]. % 10.13/10.32 congruence. % 10.13/10.32 cut (((op (e0) (e1)) = (e3)) = ((op (e0) (op (e0) (e0))) = (e3))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H25b. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H119. % 10.13/10.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.32 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25c]. % 10.13/10.32 congruence. % 10.13/10.32 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.13/10.32 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e1)) = (op (e0) (op (e0) (e0))))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H25c. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H25d. % 10.13/10.32 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.13/10.32 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H254]. % 10.13/10.32 congruence. % 10.13/10.32 apply (zenon_L200_); trivial. % 10.13/10.32 apply zenon_H25e. apply refl_equal. % 10.13/10.32 apply zenon_H25e. apply refl_equal. % 10.13/10.32 apply zenon_Heb. apply refl_equal. % 10.13/10.32 apply zenon_H84. apply refl_equal. % 10.13/10.32 apply zenon_H257. apply refl_equal. % 10.13/10.32 apply zenon_H257. apply refl_equal. % 10.13/10.32 apply zenon_H87. apply refl_equal. % 10.13/10.32 apply zenon_H257. apply refl_equal. % 10.13/10.32 apply zenon_H257. apply refl_equal. % 10.13/10.32 (* end of lemma zenon_L201_ *) % 10.13/10.32 assert (zenon_L202_ : ((op (e3) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H136 zenon_H119 zenon_H31. % 10.13/10.32 apply (zenon_notand_s _ _ ax7); [ zenon_intro zenon_H260 | zenon_intro zenon_H25f ]. % 10.13/10.32 apply zenon_H260. apply sym_equal. exact zenon_H31. % 10.13/10.32 apply (zenon_notand_s _ _ zenon_H25f); [ zenon_intro zenon_H261 | zenon_intro zenon_H255 ]. % 10.13/10.32 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.13/10.32 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e3) = (op (e0) (op (e0) (e0))))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H261. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H25d. % 10.13/10.32 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.13/10.32 cut (((op (e0) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H25b]. % 10.13/10.32 congruence. % 10.13/10.32 cut (((op (e0) (e1)) = (e3)) = ((op (e0) (op (e0) (e0))) = (e3))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H25b. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H119. % 10.13/10.32 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.32 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25c]. % 10.13/10.32 congruence. % 10.13/10.32 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.13/10.32 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e1)) = (op (e0) (op (e0) (e0))))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H25c. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H25d. % 10.13/10.32 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.13/10.32 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H254]. % 10.13/10.32 congruence. % 10.13/10.32 apply (zenon_L200_); trivial. % 10.13/10.32 apply zenon_H25e. apply refl_equal. % 10.13/10.32 apply zenon_H25e. apply refl_equal. % 10.13/10.32 apply zenon_Heb. apply refl_equal. % 10.13/10.32 apply zenon_H25e. apply refl_equal. % 10.13/10.32 apply zenon_H25e. apply refl_equal. % 10.13/10.32 apply (zenon_L201_); trivial. % 10.13/10.32 (* end of lemma zenon_L202_ *) % 10.13/10.32 assert (zenon_L203_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e3)) = (e2))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H24e zenon_H124 zenon_He0 zenon_Hf4 zenon_Hfd zenon_H122 zenon_H115 zenon_Hef zenon_H12a zenon_Ha3 zenon_H173 zenon_Ha4 zenon_H171 zenon_H6b zenon_Hb3 zenon_H104 zenon_H9a zenon_Hfc. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.13/10.32 apply (zenon_L89_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.13/10.32 apply (zenon_L65_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.13/10.32 apply (zenon_L109_); trivial. % 10.13/10.32 apply (zenon_L196_); trivial. % 10.13/10.32 (* end of lemma zenon_L203_ *) % 10.13/10.32 assert (zenon_L204_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.13/10.32 do 0 intro. intros zenon_Hb6 zenon_H1f zenon_H94 zenon_Hfc zenon_H104 zenon_Hb3 zenon_H6b zenon_H171 zenon_Ha4 zenon_H173 zenon_Ha3 zenon_H12a zenon_H115 zenon_H122 zenon_Hfd zenon_Hf4 zenon_He0 zenon_H124 zenon_H24e zenon_H99 zenon_Hef. % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.32 apply (zenon_L33_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.32 exact (zenon_H6b zenon_H6f). % 10.13/10.32 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.32 apply (zenon_L203_); trivial. % 10.13/10.32 apply (zenon_L71_); trivial. % 10.13/10.32 (* end of lemma zenon_L204_ *) % 10.13/10.32 assert (zenon_L205_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H1a3 zenon_H85 zenon_H24e zenon_H124 zenon_He0 zenon_H122 zenon_H12a zenon_H173 zenon_H171 zenon_Hfc zenon_Hf4 zenon_H15e zenon_He9 zenon_Hef zenon_H99 zenon_Hb3 zenon_H6b zenon_H115 zenon_Ha3 zenon_H94 zenon_H1f zenon_Hb6 zenon_H104 zenon_H16e zenon_Hfd. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.13/10.32 apply (zenon_L29_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.13/10.32 apply (zenon_L204_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.13/10.32 apply (zenon_L189_); trivial. % 10.13/10.32 apply (zenon_L190_); trivial. % 10.13/10.32 (* end of lemma zenon_L205_ *) % 10.13/10.32 assert (zenon_L206_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H1b0 zenon_H76. % 10.13/10.32 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb9. zenon_intro zenon_H1b1. % 10.13/10.32 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H71. zenon_intro zenon_H2a. % 10.13/10.32 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.13/10.32 exact (zenon_H76 zenon_H79). % 10.13/10.32 (* end of lemma zenon_L206_ *) % 10.13/10.32 assert (zenon_L207_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H1b7 zenon_H94 zenon_H6a. % 10.13/10.32 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.13/10.32 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H163. zenon_intro zenon_H2e. % 10.13/10.32 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.13/10.32 apply (zenon_L115_); trivial. % 10.13/10.32 (* end of lemma zenon_L207_ *) % 10.13/10.32 assert (zenon_L208_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H262 zenon_H36 zenon_H175. % 10.13/10.32 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H262. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H36. % 10.13/10.32 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 10.13/10.32 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 10.13/10.32 congruence. % 10.13/10.32 apply zenon_H172. apply refl_equal. % 10.13/10.32 apply zenon_H185. apply sym_equal. exact zenon_H175. % 10.13/10.32 (* end of lemma zenon_L208_ *) % 10.13/10.32 assert (zenon_L209_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H157 zenon_H56 zenon_Hc7. % 10.13/10.32 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H157. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H56. % 10.13/10.32 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 10.13/10.32 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.13/10.32 congruence. % 10.13/10.32 apply zenon_H5d. apply refl_equal. % 10.13/10.32 apply zenon_Hc8. apply sym_equal. exact zenon_Hc7. % 10.13/10.32 (* end of lemma zenon_L209_ *) % 10.13/10.32 assert (zenon_L210_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e3)) = (e1)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H157 zenon_H198 zenon_H107. % 10.13/10.32 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e2) (e3)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H157. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H198. % 10.13/10.32 cut (((e1) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 10.13/10.32 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.13/10.32 congruence. % 10.13/10.32 apply zenon_H5d. apply refl_equal. % 10.13/10.32 apply zenon_H123. apply sym_equal. exact zenon_H107. % 10.13/10.32 (* end of lemma zenon_L210_ *) % 10.13/10.32 assert (zenon_L211_ : ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H13b zenon_H152 zenon_H135. % 10.13/10.32 elim (classic ((op (e3) (e0)) = (op (e3) (e0)))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ]. % 10.13/10.32 cut (((op (e3) (e0)) = (op (e3) (e0))) = ((op (e2) (e0)) = (op (e3) (e0)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H135. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H13e. % 10.13/10.32 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 10.13/10.32 cut (((op (e3) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H263]. % 10.13/10.32 congruence. % 10.13/10.32 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e2) (e0)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H263. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H13b. % 10.13/10.32 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 10.13/10.32 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 10.13/10.32 congruence. % 10.13/10.32 apply zenon_H13f. apply refl_equal. % 10.13/10.32 apply zenon_H264. apply sym_equal. exact zenon_H152. % 10.13/10.32 apply zenon_H13f. apply refl_equal. % 10.13/10.32 apply zenon_H13f. apply refl_equal. % 10.13/10.32 (* end of lemma zenon_L211_ *) % 10.13/10.32 assert (zenon_L212_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H100 zenon_H119 zenon_H120. % 10.13/10.32 cut (((op (e0) (e1)) = (e3)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H100. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H119. % 10.13/10.32 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H156]. % 10.13/10.32 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 10.13/10.32 congruence. % 10.13/10.32 apply zenon_H39. apply refl_equal. % 10.13/10.32 apply zenon_H156. apply sym_equal. exact zenon_H120. % 10.13/10.32 (* end of lemma zenon_L212_ *) % 10.13/10.32 assert (zenon_L213_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H24b zenon_He5 zenon_Hdd. % 10.13/10.32 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_H24b. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_He5. % 10.13/10.32 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 10.13/10.32 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.13/10.32 congruence. % 10.13/10.32 apply zenon_H5d. apply refl_equal. % 10.13/10.32 apply zenon_H265. apply sym_equal. exact zenon_Hdd. % 10.13/10.32 (* end of lemma zenon_L213_ *) % 10.13/10.32 assert (zenon_L214_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> False). % 10.13/10.32 do 0 intro. intros zenon_Hc6 zenon_H17c zenon_H159. % 10.13/10.32 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e2) (e3)))). % 10.13/10.32 intro zenon_D_pnotp. % 10.13/10.32 apply zenon_Hc6. % 10.13/10.32 rewrite <- zenon_D_pnotp. % 10.13/10.32 exact zenon_H17c. % 10.13/10.32 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H15a]. % 10.13/10.32 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 10.13/10.32 congruence. % 10.13/10.32 apply zenon_Hc9. apply refl_equal. % 10.13/10.32 apply zenon_H15a. apply sym_equal. exact zenon_H159. % 10.13/10.32 (* end of lemma zenon_L214_ *) % 10.13/10.32 assert (zenon_L215_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H266 zenon_Hc7 zenon_H115 zenon_H36 zenon_He5 zenon_H24b zenon_Hc6 zenon_H159. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H267 ]. % 10.13/10.32 apply (zenon_L46_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_Hef | zenon_intro zenon_H268 ]. % 10.13/10.32 apply (zenon_L65_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hdd | zenon_intro zenon_H17c ]. % 10.13/10.32 apply (zenon_L213_); trivial. % 10.13/10.32 apply (zenon_L214_); trivial. % 10.13/10.32 (* end of lemma zenon_L215_ *) % 10.13/10.32 assert (zenon_L216_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.32 do 0 intro. intros zenon_H15b zenon_H135 zenon_H13b zenon_H119 zenon_H100 zenon_H107 zenon_H9a zenon_H266 zenon_Hc7 zenon_H115 zenon_H36 zenon_He5 zenon_H24b zenon_Hc6. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.13/10.32 apply (zenon_L211_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.13/10.32 apply (zenon_L212_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.13/10.32 apply (zenon_L64_); trivial. % 10.13/10.32 apply (zenon_L215_); trivial. % 10.13/10.32 (* end of lemma zenon_L216_ *) % 10.13/10.32 assert (zenon_L217_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 10.13/10.32 do 0 intro. intros zenon_H124 zenon_H31 zenon_Hc0 zenon_H36 zenon_H171 zenon_H163 zenon_H15b zenon_H135 zenon_H13b zenon_Hfd zenon_Hc3 zenon_H9a zenon_H157 zenon_H158. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.32 apply (zenon_L121_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.32 apply (zenon_L107_); trivial. % 10.13/10.32 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.32 exact (zenon_H163 zenon_H103). % 10.13/10.32 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.13/10.33 apply (zenon_L211_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.13/10.33 apply (zenon_L73_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.13/10.33 apply (zenon_L64_); trivial. % 10.13/10.33 apply (zenon_L94_); trivial. % 10.13/10.33 (* end of lemma zenon_L217_ *) % 10.13/10.33 assert (zenon_L218_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H269 zenon_Hc6 zenon_H24b zenon_H115 zenon_Hc7 zenon_H266 zenon_H107 zenon_H100 zenon_H119 zenon_H124 zenon_H31 zenon_Hc0 zenon_H36 zenon_H171 zenon_H163 zenon_H15b zenon_H135 zenon_H13b zenon_Hfd zenon_Hc3 zenon_H9a zenon_H157. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H56 | zenon_intro zenon_H26a ]. % 10.13/10.33 apply (zenon_L209_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H198 | zenon_intro zenon_H26b ]. % 10.13/10.33 apply (zenon_L210_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_He5 | zenon_intro zenon_H158 ]. % 10.13/10.33 apply (zenon_L216_); trivial. % 10.13/10.33 apply (zenon_L217_); trivial. % 10.13/10.33 (* end of lemma zenon_L218_ *) % 10.13/10.33 assert (zenon_L219_ : (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H104 zenon_H1ed zenon_H187. % 10.13/10.33 cut (((op (e3) (e2)) = (e3)) = ((e1) = (e3))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H104. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H1ed. % 10.13/10.33 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.33 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H26c]. % 10.13/10.33 congruence. % 10.13/10.33 exact (zenon_H26c zenon_H187). % 10.13/10.33 apply zenon_Heb. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L219_ *) % 10.13/10.33 assert (zenon_L220_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1de zenon_H131 zenon_H128. % 10.13/10.33 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H1de. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H131. % 10.13/10.33 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26d]. % 10.13/10.33 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_H13f. apply refl_equal. % 10.13/10.33 apply zenon_H26d. apply sym_equal. exact zenon_H128. % 10.13/10.33 (* end of lemma zenon_L220_ *) % 10.13/10.33 assert (zenon_L221_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H67 zenon_H13b zenon_H26e. % 10.13/10.33 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.13/10.33 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H26e. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Hd6. % 10.13/10.33 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.33 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H26f. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H67. % 10.13/10.33 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 10.13/10.33 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_Hd7. apply refl_equal. % 10.13/10.33 apply zenon_H1e0. apply sym_equal. exact zenon_H13b. % 10.13/10.33 apply zenon_Hd7. apply refl_equal. % 10.13/10.33 apply zenon_Hd7. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L221_ *) % 10.13/10.33 assert (zenon_L222_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H145 zenon_H128 zenon_H1de zenon_H130 zenon_H31 zenon_H119 zenon_H67 zenon_H26e. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H131 | zenon_intro zenon_H146 ]. % 10.13/10.33 apply (zenon_L220_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H133 | zenon_intro zenon_H147 ]. % 10.13/10.33 apply (zenon_L82_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H136 | zenon_intro zenon_H13b ]. % 10.13/10.33 apply (zenon_L202_); trivial. % 10.13/10.33 apply (zenon_L221_); trivial. % 10.13/10.33 (* end of lemma zenon_L222_ *) % 10.13/10.33 assert (zenon_L223_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e3)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H244 zenon_H157 zenon_H9a zenon_Hc3 zenon_Hfd zenon_H135 zenon_H15b zenon_H163 zenon_H171 zenon_H36 zenon_Hc0 zenon_H124 zenon_H100 zenon_H107 zenon_H266 zenon_Hc7 zenon_H115 zenon_H24b zenon_Hc6 zenon_H269 zenon_He9 zenon_H187 zenon_H104 zenon_H145 zenon_H128 zenon_H1de zenon_H130 zenon_H31 zenon_H119 zenon_H26e. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.13/10.33 apply (zenon_L218_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.13/10.33 apply (zenon_L77_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.13/10.33 apply (zenon_L219_); trivial. % 10.13/10.33 apply (zenon_L222_); trivial. % 10.13/10.33 (* end of lemma zenon_L223_ *) % 10.13/10.33 assert (zenon_L224_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_Hca zenon_H1f zenon_H85 zenon_H71 zenon_Hf4 zenon_H18a zenon_H262 zenon_H26e zenon_H119 zenon_H31 zenon_H130 zenon_H1de zenon_H128 zenon_H145 zenon_H104 zenon_He9 zenon_H269 zenon_Hc6 zenon_H24b zenon_H115 zenon_H266 zenon_H100 zenon_H124 zenon_Hc0 zenon_H36 zenon_H171 zenon_H163 zenon_H15b zenon_H135 zenon_Hfd zenon_Hc3 zenon_H9a zenon_H157 zenon_H244 zenon_Hd5. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.13/10.33 apply (zenon_L44_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.13/10.33 apply (zenon_L45_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.13/10.33 exact (zenon_H71 zenon_H74). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.33 apply (zenon_L121_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.33 apply (zenon_L193_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.33 exact (zenon_H163 zenon_H103). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.13/10.33 apply (zenon_L82_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.13/10.33 apply (zenon_L208_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.13/10.33 apply (zenon_L223_); trivial. % 10.13/10.33 apply (zenon_L126_); trivial. % 10.13/10.33 (* end of lemma zenon_L224_ *) % 10.13/10.33 assert (zenon_L225_ : ((op (e1) (e1)) = (e1)) -> ((op (e1) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H36 zenon_Ha2 zenon_H104. % 10.13/10.33 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.33 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H104. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Hea. % 10.13/10.33 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.33 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e1) (e1)) = (e1)) = ((e3) = (e1))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H105. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H36. % 10.13/10.33 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.33 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 10.13/10.33 congruence. % 10.13/10.33 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.33 apply zenon_H98. apply refl_equal. % 10.13/10.33 apply zenon_Heb. apply refl_equal. % 10.13/10.33 apply zenon_Heb. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L225_ *) % 10.13/10.33 assert (zenon_L226_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H124 zenon_H31 zenon_Hc0 zenon_Hc3 zenon_Hf4 zenon_H163 zenon_Hc6 zenon_Hef. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.33 apply (zenon_L121_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.33 apply (zenon_L193_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.33 exact (zenon_H163 zenon_H103). % 10.13/10.33 apply (zenon_L75_); trivial. % 10.13/10.33 (* end of lemma zenon_L226_ *) % 10.13/10.33 assert (zenon_L227_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1b7 zenon_H124 zenon_Hc0 zenon_Hf4 zenon_Hc6 zenon_Hef. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H163. zenon_intro zenon_H2e. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.13/10.33 apply (zenon_L226_); trivial. % 10.13/10.33 (* end of lemma zenon_L227_ *) % 10.13/10.33 assert (zenon_L228_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H124 zenon_H31 zenon_Hc0 zenon_H36 zenon_H171 zenon_H163 zenon_H189 zenon_Hd5. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.33 apply (zenon_L121_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.33 apply (zenon_L107_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.33 exact (zenon_H163 zenon_H103). % 10.13/10.33 apply (zenon_L126_); trivial. % 10.13/10.33 (* end of lemma zenon_L228_ *) % 10.13/10.33 assert (zenon_L229_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H16f zenon_H6a zenon_H138. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hef. zenon_intro zenon_H170. % 10.13/10.33 apply (zenon_L84_); trivial. % 10.13/10.33 (* end of lemma zenon_L229_ *) % 10.13/10.33 assert (zenon_L230_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1ac zenon_H6a. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_Hb9. zenon_intro zenon_H1ad. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H71. zenon_intro zenon_H24. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.13/10.33 exact (zenon_H6e zenon_H6a). % 10.13/10.33 (* end of lemma zenon_L230_ *) % 10.13/10.33 assert (zenon_L231_ : (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> False). % 10.13/10.33 do 0 intro. intros zenon_Hbb zenon_H6a zenon_Hfa. % 10.13/10.33 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e2) (e0)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_Hbb. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H6a. % 10.13/10.33 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 10.13/10.33 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H270]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_H270. apply refl_equal. % 10.13/10.33 apply zenon_H181. apply sym_equal. exact zenon_Hfa. % 10.13/10.33 (* end of lemma zenon_L231_ *) % 10.13/10.33 assert (zenon_L232_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H124 zenon_H6a zenon_Hbb zenon_Hc3 zenon_Hf4 zenon_H163 zenon_H189 zenon_Hd5. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.33 apply (zenon_L231_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.33 apply (zenon_L193_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.33 exact (zenon_H163 zenon_H103). % 10.13/10.33 apply (zenon_L126_); trivial. % 10.13/10.33 (* end of lemma zenon_L232_ *) % 10.13/10.33 assert (zenon_L233_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1c9 zenon_H1f zenon_He9. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_Hd4. zenon_intro zenon_H1ca. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1ca). zenon_intro zenon_Hff. zenon_intro zenon_H57. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.13/10.33 apply (zenon_L54_); trivial. % 10.13/10.33 (* end of lemma zenon_L233_ *) % 10.13/10.33 assert (zenon_L234_ : (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H85 zenon_Hd4 zenon_Hc7. % 10.13/10.33 cut (((op (e2) (e3)) = (e2)) = ((e0) = (e2))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H85. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Hd4. % 10.13/10.33 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.33 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H271]. % 10.13/10.33 congruence. % 10.13/10.33 exact (zenon_H271 zenon_Hc7). % 10.13/10.33 apply zenon_H87. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L234_ *) % 10.13/10.33 assert (zenon_L235_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H272 zenon_H5b zenon_H1f zenon_Ha2 zenon_Ha4 zenon_Hd4 zenon_H85 zenon_H76. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.13/10.33 apply (zenon_L16_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.13/10.33 apply (zenon_L40_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.13/10.33 apply (zenon_L234_); trivial. % 10.13/10.33 exact (zenon_H76 zenon_H79). % 10.13/10.33 (* end of lemma zenon_L235_ *) % 10.13/10.33 assert (zenon_L236_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H6a zenon_Hba zenon_Hf4. % 10.13/10.33 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.13/10.33 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_Hf4. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H86. % 10.13/10.33 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.33 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e1) (e0)) = (e1)) = ((e2) = (e1))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_Hf5. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H6a. % 10.13/10.33 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.33 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H275]. % 10.13/10.33 congruence. % 10.13/10.33 exact (zenon_H275 zenon_Hba). % 10.13/10.33 apply zenon_H98. apply refl_equal. % 10.13/10.33 apply zenon_H87. apply refl_equal. % 10.13/10.33 apply zenon_H87. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L236_ *) % 10.13/10.33 assert (zenon_L237_ : ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H91 zenon_Ha2 zenon_Hfd. % 10.13/10.33 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.33 cut (((e3) = (e3)) = ((e2) = (e3))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_Hfd. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Hea. % 10.13/10.33 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.33 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e1) (e1)) = (e2)) = ((e3) = (e2))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_Hfe. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H91. % 10.13/10.33 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.33 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 10.13/10.33 congruence. % 10.13/10.33 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.33 apply zenon_H87. apply refl_equal. % 10.13/10.33 apply zenon_Heb. apply refl_equal. % 10.13/10.33 apply zenon_Heb. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L237_ *) % 10.13/10.33 assert (zenon_L238_ : ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_Hd4 zenon_Hdd zenon_Hc6. % 10.13/10.33 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cd ]. % 10.13/10.33 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_Hc6. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H1cc. % 10.13/10.33 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 10.13/10.33 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H276. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Hd4. % 10.13/10.33 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 10.13/10.33 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_H1cd. apply refl_equal. % 10.13/10.33 apply zenon_H265. apply sym_equal. exact zenon_Hdd. % 10.13/10.33 apply zenon_H1cd. apply refl_equal. % 10.13/10.33 apply zenon_H1cd. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L238_ *) % 10.13/10.33 assert (zenon_L239_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_Hdf zenon_Hf4 zenon_H6a zenon_Hfd zenon_Ha2 zenon_Hcd zenon_Hda zenon_Hd4 zenon_Hc6. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.13/10.33 apply (zenon_L236_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.13/10.33 apply (zenon_L237_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.13/10.33 apply (zenon_L50_); trivial. % 10.13/10.33 apply (zenon_L238_); trivial. % 10.13/10.33 (* end of lemma zenon_L239_ *) % 10.13/10.33 assert (zenon_L240_ : ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_Hd4 zenon_He5 zenon_H157. % 10.13/10.33 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cd ]. % 10.13/10.33 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H157. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H1cc. % 10.13/10.33 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 10.13/10.33 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H277. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Hd4. % 10.13/10.33 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He8]. % 10.13/10.33 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_H1cd. apply refl_equal. % 10.13/10.33 apply zenon_He8. apply sym_equal. exact zenon_He5. % 10.13/10.33 apply zenon_H1cd. apply refl_equal. % 10.13/10.33 apply zenon_H1cd. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L240_ *) % 10.13/10.33 assert (zenon_L241_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> ((op (e1) (e0)) = (e1)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1d8 zenon_H6a. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1d8). zenon_intro zenon_H13b. zenon_intro zenon_H1d9. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1d9). zenon_intro zenon_H76. zenon_intro zenon_H24. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.13/10.33 exact (zenon_H6e zenon_H6a). % 10.13/10.33 (* end of lemma zenon_L241_ *) % 10.13/10.33 assert (zenon_L242_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> (~((op (e2) (e2)) = (e0))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1da zenon_H71. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_H13b. zenon_intro zenon_H1db. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1db). zenon_intro zenon_H76. zenon_intro zenon_H27. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.13/10.33 exact (zenon_H71 zenon_H74). % 10.13/10.33 (* end of lemma zenon_L242_ *) % 10.13/10.33 assert (zenon_L243_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1e1 zenon_H94 zenon_H6a. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H127. zenon_intro zenon_H1e2. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H1e5. zenon_intro zenon_H2e. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.13/10.33 apply (zenon_L115_); trivial. % 10.13/10.33 (* end of lemma zenon_L243_ *) % 10.13/10.33 assert (zenon_L244_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H13d zenon_H6a zenon_H133. % 10.13/10.33 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H13d. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H6a. % 10.13/10.33 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 10.13/10.33 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H270]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_H270. apply refl_equal. % 10.13/10.33 apply zenon_H134. apply sym_equal. exact zenon_H133. % 10.13/10.33 (* end of lemma zenon_L244_ *) % 10.13/10.33 assert (zenon_L245_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H278 zenon_H103 zenon_H187. % 10.13/10.33 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H278. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H103. % 10.13/10.33 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 10.13/10.33 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_Hd0. apply refl_equal. % 10.13/10.33 apply zenon_H188. apply sym_equal. exact zenon_H187. % 10.13/10.33 (* end of lemma zenon_L245_ *) % 10.13/10.33 assert (zenon_L246_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1eb zenon_H1f zenon_H85. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ed. zenon_intro zenon_H1ec. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ee. zenon_intro zenon_H43. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.13/10.33 apply (zenon_L29_); trivial. % 10.13/10.33 (* end of lemma zenon_L246_ *) % 10.13/10.33 assert (zenon_L247_ : ((op (e1) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H6f zenon_H91 zenon_H85. % 10.13/10.33 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.13/10.33 cut (((e2) = (e2)) = ((e0) = (e2))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H85. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H86. % 10.13/10.33 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.33 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e1) (e1)) = (e0)) = ((e2) = (e0))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H88. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H6f. % 10.13/10.33 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.33 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 10.13/10.33 congruence. % 10.13/10.33 exact (zenon_H8c zenon_H91). % 10.13/10.33 apply zenon_H84. apply refl_equal. % 10.13/10.33 apply zenon_H87. apply refl_equal. % 10.13/10.33 apply zenon_H87. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L247_ *) % 10.13/10.33 assert (zenon_L248_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H6a zenon_H13c zenon_H104. % 10.13/10.33 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.33 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H104. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Hea. % 10.13/10.33 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.33 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e1) (e0)) = (e1)) = ((e3) = (e1))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H105. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H6a. % 10.13/10.33 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.33 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 10.13/10.33 congruence. % 10.13/10.33 exact (zenon_H279 zenon_H13c). % 10.13/10.33 apply zenon_H98. apply refl_equal. % 10.13/10.33 apply zenon_Heb. apply refl_equal. % 10.13/10.33 apply zenon_Heb. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L248_ *) % 10.13/10.33 assert (zenon_L249_ : ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1ed zenon_H17a zenon_H186. % 10.13/10.33 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ]. % 10.13/10.33 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H186. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H1f0. % 10.13/10.33 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 10.13/10.33 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H27a. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H1ed. % 10.13/10.33 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 10.13/10.33 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_H1f1. apply refl_equal. % 10.13/10.33 apply zenon_H27b. apply sym_equal. exact zenon_H17a. % 10.13/10.33 apply zenon_H1f1. apply refl_equal. % 10.13/10.33 apply zenon_H1f1. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L249_ *) % 10.13/10.33 assert (zenon_L250_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H17e zenon_H104 zenon_H6a zenon_Hfd zenon_H91 zenon_H186 zenon_H1ed zenon_Ha5 zenon_He9. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.33 apply (zenon_L248_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.33 apply (zenon_L237_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.33 apply (zenon_L249_); trivial. % 10.13/10.33 apply (zenon_L119_); trivial. % 10.13/10.33 (* end of lemma zenon_L250_ *) % 10.13/10.33 assert (zenon_L251_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.13/10.33 do 0 intro. intros zenon_Hb6 zenon_H1f zenon_H94 zenon_H85 zenon_H119 zenon_H17e zenon_H104 zenon_H6a zenon_Hfd zenon_H91 zenon_H186 zenon_H1ed zenon_He9. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.33 apply (zenon_L33_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.33 apply (zenon_L247_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.33 apply (zenon_L69_); trivial. % 10.13/10.33 apply (zenon_L250_); trivial. % 10.13/10.33 (* end of lemma zenon_L251_ *) % 10.13/10.33 assert (zenon_L252_ : ((op (e3) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1ed zenon_H150 zenon_H27c. % 10.13/10.33 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ]. % 10.13/10.33 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H27c. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H1f0. % 10.13/10.33 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 10.13/10.33 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27d]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H27d. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H1ed. % 10.13/10.33 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 10.13/10.33 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_H1f1. apply refl_equal. % 10.13/10.33 apply zenon_H27e. apply sym_equal. exact zenon_H150. % 10.13/10.33 apply zenon_H1f1. apply refl_equal. % 10.13/10.33 apply zenon_H1f1. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L252_ *) % 10.13/10.33 assert (zenon_L253_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H24b zenon_H158 zenon_H17c. % 10.13/10.33 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H24b. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H158. % 10.13/10.33 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H27f]. % 10.13/10.33 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_H5d. apply refl_equal. % 10.13/10.33 apply zenon_H27f. apply sym_equal. exact zenon_H17c. % 10.13/10.33 (* end of lemma zenon_L253_ *) % 10.13/10.33 assert (zenon_L254_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H17e zenon_H104 zenon_H6a zenon_Hfd zenon_H91 zenon_H186 zenon_H1ed zenon_H24b zenon_H158. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.33 apply (zenon_L248_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.33 apply (zenon_L237_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.33 apply (zenon_L249_); trivial. % 10.13/10.33 apply (zenon_L253_); trivial. % 10.13/10.33 (* end of lemma zenon_L254_ *) % 10.13/10.33 assert (zenon_L255_ : (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> False). % 10.13/10.33 do 0 intro. intros zenon_Hfd zenon_H13b zenon_H136. % 10.13/10.33 cut (((op (e3) (e0)) = (e3)) = ((e2) = (e3))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_Hfd. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H13b. % 10.13/10.33 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.33 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H280]. % 10.13/10.33 congruence. % 10.13/10.33 exact (zenon_H280 zenon_H136). % 10.13/10.33 apply zenon_Heb. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L255_ *) % 10.13/10.33 assert (zenon_L256_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H281 zenon_H85 zenon_H1f zenon_Hf4 zenon_H6a zenon_H1b2 zenon_Hc3 zenon_Hfd zenon_H13b. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.13/10.33 apply (zenon_L29_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.13/10.33 apply (zenon_L236_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.13/10.33 apply (zenon_L152_); trivial. % 10.13/10.33 apply (zenon_L255_); trivial. % 10.13/10.33 (* end of lemma zenon_L256_ *) % 10.13/10.33 assert (zenon_L257_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H171 zenon_Ha2 zenon_H120. % 10.13/10.33 cut (((op (e1) (e1)) = (e3)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H171. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Ha2. % 10.13/10.33 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H156]. % 10.13/10.33 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_H172. apply refl_equal. % 10.13/10.33 apply zenon_H156. apply sym_equal. exact zenon_H120. % 10.13/10.33 (* end of lemma zenon_L257_ *) % 10.13/10.33 assert (zenon_L258_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H198 zenon_H16e zenon_H284. % 10.13/10.33 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 10.13/10.33 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e2)) = (op (e0) (e3)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H284. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H5c. % 10.13/10.33 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.13/10.33 cut (((op (e0) (e3)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H285]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e0) (e2)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H285. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H198. % 10.13/10.33 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 10.13/10.33 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_H5d. apply refl_equal. % 10.13/10.33 apply zenon_H195. apply sym_equal. exact zenon_H16e. % 10.13/10.33 apply zenon_H5d. apply refl_equal. % 10.13/10.33 apply zenon_H5d. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L258_ *) % 10.13/10.33 assert (zenon_L259_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1b2 zenon_Hc1 zenon_Hc4. % 10.13/10.33 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H1b2. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Hc1. % 10.13/10.33 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H286]. % 10.13/10.33 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_Hbd. apply refl_equal. % 10.13/10.33 apply zenon_H286. apply sym_equal. exact zenon_Hc4. % 10.13/10.33 (* end of lemma zenon_L259_ *) % 10.13/10.33 assert (zenon_L260_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H103 zenon_Hfa zenon_H287. % 10.13/10.33 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd0 ]. % 10.13/10.33 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e2) (e0)) = (op (e2) (e2)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H287. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Hcf. % 10.13/10.33 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.33 cut (((op (e2) (e2)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e2) (e2)) = (e1)) = ((op (e2) (e2)) = (op (e2) (e0)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H288. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H103. % 10.13/10.33 cut (((e1) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 10.13/10.33 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_Hd0. apply refl_equal. % 10.13/10.33 apply zenon_H181. apply sym_equal. exact zenon_Hfa. % 10.13/10.33 apply zenon_Hd0. apply refl_equal. % 10.13/10.33 apply zenon_Hd0. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L260_ *) % 10.13/10.33 assert (zenon_L261_ : ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6a zenon_H94 zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef zenon_H13b. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.13/10.33 apply (zenon_L1_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.13/10.33 apply (zenon_L2_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.13/10.33 apply (zenon_L3_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.13/10.33 apply (zenon_L4_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.13/10.33 apply (zenon_L5_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.13/10.33 apply (zenon_L6_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.13/10.33 apply (zenon_L8_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.13/10.33 apply (zenon_L9_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.13/10.33 apply (zenon_L10_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.13/10.33 apply (zenon_L12_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.13/10.33 apply (zenon_L13_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.13/10.33 apply (zenon_L14_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.13/10.33 apply (zenon_L15_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.13/10.33 apply (zenon_L17_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.13/10.33 apply (zenon_L18_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.13/10.33 apply (zenon_L19_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.13/10.33 apply (zenon_L20_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.13/10.33 apply (zenon_L21_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.13/10.33 apply (zenon_L112_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.13/10.33 apply (zenon_L113_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.13/10.33 apply (zenon_L24_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.13/10.33 apply (zenon_L25_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.13/10.33 apply (zenon_L26_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.13/10.33 apply (zenon_L27_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.13/10.33 apply (zenon_L114_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.13/10.33 apply (zenon_L31_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.13/10.33 apply (zenon_L32_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.13/10.33 apply (zenon_L129_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.13/10.33 apply (zenon_L145_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.13/10.33 apply (zenon_L56_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.13/10.33 apply (zenon_L229_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.13/10.33 apply (zenon_L147_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.13/10.33 apply (zenon_L148_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.13/10.33 apply (zenon_L230_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.13/10.33 apply (zenon_L150_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.13/10.33 apply (zenon_L151_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.13/10.33 apply (zenon_L207_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.13/10.33 apply (zenon_L154_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.13/10.33 apply (zenon_L155_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.13/10.33 apply (zenon_L156_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.13/10.33 apply (zenon_L157_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.13/10.33 apply (zenon_L158_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.13/10.33 apply (zenon_L159_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.13/10.33 apply (zenon_L160_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.13/10.33 apply (zenon_L161_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.13/10.33 apply (zenon_L163_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.13/10.33 apply (zenon_L164_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.13/10.33 apply (zenon_L165_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.13/10.33 apply (zenon_L166_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.13/10.33 apply (zenon_L241_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.13/10.33 apply (zenon_L168_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.13/10.33 apply (zenon_L169_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.13/10.33 apply (zenon_L243_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.13/10.33 apply (zenon_L172_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.13/10.33 apply (zenon_L173_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.13/10.33 apply (zenon_L174_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.13/10.33 apply (zenon_L175_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.13/10.33 apply (zenon_L177_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.13/10.33 apply (zenon_L178_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.13/10.33 apply (zenon_L179_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.13/10.33 apply (zenon_L180_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.13/10.33 apply (zenon_L181_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.13/10.33 apply (zenon_L182_); trivial. % 10.13/10.33 apply (zenon_L183_); trivial. % 10.13/10.33 (* end of lemma zenon_L261_ *) % 10.13/10.33 assert (zenon_L262_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H289 zenon_He9 zenon_H104 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6a zenon_H94 zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.13/10.33 apply (zenon_L54_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.13/10.33 apply (zenon_L248_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.13/10.33 apply (zenon_L92_); trivial. % 10.13/10.33 apply (zenon_L261_); trivial. % 10.13/10.33 (* end of lemma zenon_L262_ *) % 10.13/10.33 assert (zenon_L263_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H28c zenon_Hc4 zenon_H287 zenon_H103 zenon_H1ef zenon_Hc0 zenon_H1de zenon_H94 zenon_H6a zenon_H1cb zenon_H130 zenon_H1b2 zenon_H138 zenon_H18d zenon_H1f zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_H104 zenon_He9 zenon_H289 zenon_H13b zenon_H135. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H28d ]. % 10.13/10.33 apply (zenon_L259_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_Hfa | zenon_intro zenon_H28e ]. % 10.13/10.33 apply (zenon_L260_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H152 ]. % 10.13/10.33 apply (zenon_L262_); trivial. % 10.13/10.33 apply (zenon_L211_); trivial. % 10.13/10.33 (* end of lemma zenon_L263_ *) % 10.13/10.33 assert (zenon_L264_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H28f zenon_H51 zenon_Hd4. % 10.13/10.33 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H28f. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H51. % 10.13/10.33 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 10.13/10.33 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_Hd0. apply refl_equal. % 10.13/10.33 apply zenon_Hd9. apply sym_equal. exact zenon_Hd4. % 10.13/10.33 (* end of lemma zenon_L264_ *) % 10.13/10.33 assert (zenon_L265_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H1cf zenon_H28f zenon_H51. % 10.13/10.33 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_Hd4. zenon_intro zenon_H1d0. % 10.13/10.33 apply (zenon_L264_); trivial. % 10.13/10.33 (* end of lemma zenon_L265_ *) % 10.13/10.33 assert (zenon_L266_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (~((op (e2) (e2)) = (e3))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H290 zenon_H71 zenon_H187 zenon_H278 zenon_H28f zenon_H1cf zenon_Hff. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H74 | zenon_intro zenon_H291 ]. % 10.13/10.33 exact (zenon_H71 zenon_H74). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H103 | zenon_intro zenon_H292 ]. % 10.13/10.33 apply (zenon_L245_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfc ]. % 10.13/10.33 apply (zenon_L265_); trivial. % 10.13/10.33 exact (zenon_Hff zenon_Hfc). % 10.13/10.33 (* end of lemma zenon_L266_ *) % 10.13/10.33 assert (zenon_L267_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (~((op (e2) (e2)) = (e3))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H293 zenon_H284 zenon_H198 zenon_H135 zenon_H13b zenon_H289 zenon_He9 zenon_H104 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6a zenon_H94 zenon_H1de zenon_Hc0 zenon_H1ef zenon_H287 zenon_Hc4 zenon_H28c zenon_H290 zenon_H71 zenon_H278 zenon_H28f zenon_H1cf zenon_Hff. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.13/10.33 apply (zenon_L258_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.13/10.33 apply (zenon_L128_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.13/10.33 apply (zenon_L263_); trivial. % 10.13/10.33 apply (zenon_L266_); trivial. % 10.13/10.33 (* end of lemma zenon_L267_ *) % 10.13/10.33 assert (zenon_L268_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 10.13/10.33 do 0 intro. intros zenon_Hca zenon_Hff zenon_H1cf zenon_H28f zenon_H278 zenon_H290 zenon_H28c zenon_H287 zenon_H1ef zenon_Hc0 zenon_H1de zenon_H94 zenon_H6a zenon_H1cb zenon_H130 zenon_H1b2 zenon_H138 zenon_H18d zenon_H1f zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_H104 zenon_He9 zenon_H289 zenon_H13b zenon_H135 zenon_H198 zenon_H284 zenon_H293 zenon_H71 zenon_H85 zenon_Hd4. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.13/10.33 apply (zenon_L44_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.13/10.33 apply (zenon_L267_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.13/10.33 exact (zenon_H71 zenon_H74). % 10.13/10.33 apply (zenon_L234_); trivial. % 10.13/10.33 (* end of lemma zenon_L268_ *) % 10.13/10.33 assert (zenon_L269_ : (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> False). % 10.13/10.33 do 0 intro. intros zenon_Hf4 zenon_Hd4 zenon_H107. % 10.13/10.33 cut (((op (e2) (e3)) = (e2)) = ((e1) = (e2))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_Hf4. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Hd4. % 10.13/10.33 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.33 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H296]. % 10.13/10.33 congruence. % 10.13/10.33 exact (zenon_H296 zenon_H107). % 10.13/10.33 apply zenon_H87. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L269_ *) % 10.13/10.33 assert (zenon_L270_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H24b zenon_H56 zenon_Ha5. % 10.13/10.33 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H24b. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H56. % 10.13/10.33 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H297]. % 10.13/10.33 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.13/10.33 congruence. % 10.13/10.33 apply zenon_H5d. apply refl_equal. % 10.13/10.33 apply zenon_H297. apply sym_equal. exact zenon_Ha5. % 10.13/10.33 (* end of lemma zenon_L270_ *) % 10.13/10.33 assert (zenon_L271_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H269 zenon_Ha5 zenon_H24b zenon_H189 zenon_He6 zenon_Hd4 zenon_H157 zenon_H159. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H56 | zenon_intro zenon_H26a ]. % 10.13/10.33 apply (zenon_L270_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H198 | zenon_intro zenon_H26b ]. % 10.13/10.33 apply (zenon_L140_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_He5 | zenon_intro zenon_H158 ]. % 10.13/10.33 apply (zenon_L240_); trivial. % 10.13/10.33 apply (zenon_L94_); trivial. % 10.13/10.33 (* end of lemma zenon_L271_ *) % 10.13/10.33 assert (zenon_L272_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 10.13/10.33 do 0 intro. intros zenon_H298 zenon_H85 zenon_H71 zenon_H293 zenon_H284 zenon_H135 zenon_H13b zenon_H289 zenon_He9 zenon_H104 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6a zenon_H94 zenon_H1de zenon_Hc0 zenon_H1ef zenon_H287 zenon_H28c zenon_H290 zenon_H278 zenon_H28f zenon_H1cf zenon_Hff zenon_Hca zenon_Hf3 zenon_Hf4 zenon_H269 zenon_Ha5 zenon_H24b zenon_He6 zenon_Hd4 zenon_H157 zenon_H159. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.13/10.33 apply (zenon_L268_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.13/10.33 exact (zenon_Hf3 zenon_Hef). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.13/10.33 apply (zenon_L269_); trivial. % 10.13/10.33 apply (zenon_L271_); trivial. % 10.13/10.33 (* end of lemma zenon_L272_ *) % 10.13/10.33 assert (zenon_L273_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H79 zenon_H189 zenon_H99. % 10.13/10.33 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H98 ]. % 10.13/10.33 cut (((e1) = (e1)) = ((e0) = (e1))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_H99. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_Hf7. % 10.13/10.33 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.33 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 10.13/10.33 congruence. % 10.13/10.33 cut (((op (e3) (e3)) = (e0)) = ((e1) = (e0))). % 10.13/10.33 intro zenon_D_pnotp. % 10.13/10.33 apply zenon_Hf8. % 10.13/10.33 rewrite <- zenon_D_pnotp. % 10.13/10.33 exact zenon_H79. % 10.13/10.33 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.33 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 10.13/10.33 congruence. % 10.13/10.33 exact (zenon_H1e5 zenon_H189). % 10.13/10.33 apply zenon_H84. apply refl_equal. % 10.13/10.33 apply zenon_H98. apply refl_equal. % 10.13/10.33 apply zenon_H98. apply refl_equal. % 10.13/10.33 (* end of lemma zenon_L273_ *) % 10.13/10.33 assert (zenon_L274_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H298 zenon_Hff zenon_H1cf zenon_H28f zenon_H278 zenon_H71 zenon_H290 zenon_H28c zenon_Hc4 zenon_H287 zenon_H1ef zenon_Hc0 zenon_H1de zenon_H94 zenon_H6a zenon_H1cb zenon_H130 zenon_H1b2 zenon_H138 zenon_H18d zenon_H1f zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_H104 zenon_He9 zenon_H289 zenon_H13b zenon_H135 zenon_H284 zenon_H293 zenon_Hf3 zenon_Hd4 zenon_Hf4 zenon_H79 zenon_H99. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.13/10.33 apply (zenon_L267_); trivial. % 10.13/10.33 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.13/10.33 exact (zenon_Hf3 zenon_Hef). % 10.13/10.33 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.13/10.33 apply (zenon_L269_); trivial. % 10.13/10.33 apply (zenon_L273_); trivial. % 10.13/10.33 (* end of lemma zenon_L274_ *) % 10.13/10.33 assert (zenon_L275_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> False). % 10.13/10.33 do 0 intro. intros zenon_H15b zenon_Ha2 zenon_H171 zenon_H272 zenon_H157 zenon_He6 zenon_H24b zenon_H269 zenon_Hca zenon_H85 zenon_H298 zenon_Hff zenon_H1cf zenon_H28f zenon_H278 zenon_H71 zenon_H290 zenon_H28c zenon_Hc4 zenon_H287 zenon_H1ef zenon_Hc0 zenon_H1de zenon_H94 zenon_H6a zenon_H1cb zenon_H130 zenon_H1b2 zenon_H138 zenon_H18d zenon_H1f zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_H104 zenon_He9 zenon_H289 zenon_H13b zenon_H135 zenon_H284 zenon_H293 zenon_Hf3 zenon_Hd4 zenon_Hf4 zenon_H99. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.13/10.34 apply (zenon_L211_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.13/10.34 apply (zenon_L257_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.13/10.34 exact (zenon_Hff zenon_Hfc). % 10.13/10.34 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.13/10.34 apply (zenon_L16_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.13/10.34 apply (zenon_L272_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.13/10.34 apply (zenon_L234_); trivial. % 10.13/10.34 apply (zenon_L274_); trivial. % 10.13/10.34 (* end of lemma zenon_L275_ *) % 10.13/10.34 assert (zenon_L276_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H1eb zenon_H13b zenon_H1ef. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ed. zenon_intro zenon_H1ec. % 10.13/10.34 apply (zenon_L176_); trivial. % 10.13/10.34 (* end of lemma zenon_L276_ *) % 10.13/10.34 assert (zenon_L277_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H281 zenon_H85 zenon_H15b zenon_H171 zenon_H272 zenon_H157 zenon_He6 zenon_H24b zenon_H269 zenon_Hca zenon_H298 zenon_H28f zenon_H278 zenon_H290 zenon_H28c zenon_H287 zenon_Hc0 zenon_H1cb zenon_H130 zenon_H1b2 zenon_H138 zenon_H18d zenon_H1f zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_H104 zenon_He9 zenon_H289 zenon_H135 zenon_H284 zenon_H293 zenon_Hf4 zenon_H99 zenon_H71 zenon_H6a zenon_H94 zenon_H1de zenon_H1ef zenon_H13b. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.13/10.34 apply (zenon_L1_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.13/10.34 apply (zenon_L2_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.13/10.34 apply (zenon_L3_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.13/10.34 apply (zenon_L4_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.13/10.34 apply (zenon_L5_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.13/10.34 apply (zenon_L6_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.13/10.34 apply (zenon_L8_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.13/10.34 apply (zenon_L9_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.13/10.34 apply (zenon_L10_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.13/10.34 apply (zenon_L12_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.13/10.34 apply (zenon_L13_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.13/10.34 apply (zenon_L14_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.13/10.34 apply (zenon_L15_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.13/10.34 apply (zenon_L17_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.13/10.34 apply (zenon_L18_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.13/10.34 apply (zenon_L19_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.13/10.34 apply (zenon_L20_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.13/10.34 apply (zenon_L21_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.13/10.34 apply (zenon_L22_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.13/10.34 apply (zenon_L113_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.13/10.34 apply (zenon_L24_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.13/10.34 apply (zenon_L25_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.13/10.34 apply (zenon_L26_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.13/10.34 apply (zenon_L27_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.13/10.34 apply (zenon_L30_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.13/10.34 apply (zenon_L31_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.13/10.34 apply (zenon_L32_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.13/10.34 apply (zenon_L129_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.13/10.34 apply (zenon_L145_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.13/10.34 apply (zenon_L56_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.13/10.34 apply (zenon_L229_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.13/10.34 apply (zenon_L147_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.13/10.34 apply (zenon_L148_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.13/10.34 apply (zenon_L230_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.13/10.34 apply (zenon_L150_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.13/10.34 apply (zenon_L151_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.13/10.34 apply (zenon_L207_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.13/10.34 apply (zenon_L154_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.13/10.34 apply (zenon_L155_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_Hc3. zenon_intro zenon_H1bf. % 10.13/10.34 apply (zenon_L256_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.13/10.34 apply (zenon_L157_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.13/10.34 apply (zenon_L158_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.13/10.34 apply (zenon_L159_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.13/10.34 apply (zenon_L160_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.13/10.34 apply (zenon_L161_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_Hd4. zenon_intro zenon_H1d0. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_Hff. zenon_intro zenon_Hf2. % 10.13/10.34 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.13/10.34 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.13/10.34 apply (zenon_L44_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.13/10.34 apply (zenon_L275_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.13/10.34 exact (zenon_H71 zenon_H74). % 10.13/10.34 apply (zenon_L234_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.13/10.34 apply (zenon_L164_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.13/10.34 apply (zenon_L165_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.13/10.34 apply (zenon_L166_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.13/10.34 apply (zenon_L241_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.13/10.34 apply (zenon_L242_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.13/10.34 apply (zenon_L169_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.13/10.34 apply (zenon_L243_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.13/10.34 apply (zenon_L172_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.13/10.34 apply (zenon_L173_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.13/10.34 apply (zenon_L174_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.13/10.34 apply (zenon_L276_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.13/10.34 apply (zenon_L177_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.13/10.34 apply (zenon_L178_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.13/10.34 apply (zenon_L179_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.13/10.34 apply (zenon_L180_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.13/10.34 apply (zenon_L181_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.13/10.34 apply (zenon_L182_); trivial. % 10.13/10.34 apply (zenon_L183_); trivial. % 10.13/10.34 (* end of lemma zenon_L277_ *) % 10.13/10.34 assert (zenon_L278_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H29b zenon_H202 zenon_H15e zenon_H24b zenon_H27c zenon_H17e zenon_H186 zenon_Hb6 zenon_H18a zenon_H278 zenon_H104 zenon_H13d zenon_H1a3 zenon_H157 zenon_Hfd zenon_Hda zenon_Hc6 zenon_Hdf zenon_H272 zenon_H124 zenon_Hd5 zenon_Hf4 zenon_Hbb zenon_H94 zenon_H138 zenon_He9 zenon_H18d zenon_H6a zenon_H85 zenon_H5b zenon_H47 zenon_H37 zenon_H1f zenon_H135 zenon_H171 zenon_H99 zenon_Hca zenon_H284 zenon_H28c zenon_H1ef zenon_H1de zenon_H1cb zenon_H289 zenon_H287 zenon_H290 zenon_H28f zenon_H293 zenon_H269 zenon_He6 zenon_H298 zenon_H15b zenon_Hc0 zenon_H281 zenon_H1b2 zenon_H130 zenon_H29c. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H29b); [ zenon_intro zenon_H71 | zenon_intro zenon_Hb9 ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H29c); [ zenon_intro zenon_H76 | zenon_intro zenon_H13b ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.13/10.34 apply (zenon_L1_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.13/10.34 apply (zenon_L2_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.13/10.34 apply (zenon_L3_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.13/10.34 apply (zenon_L4_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.13/10.34 apply (zenon_L5_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.13/10.34 apply (zenon_L6_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.13/10.34 apply (zenon_L8_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.13/10.34 apply (zenon_L9_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.13/10.34 apply (zenon_L10_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.13/10.34 apply (zenon_L12_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.13/10.34 apply (zenon_L13_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.13/10.34 apply (zenon_L14_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.13/10.34 apply (zenon_L15_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.13/10.34 apply (zenon_L17_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.13/10.34 apply (zenon_L18_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.13/10.34 apply (zenon_L19_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.13/10.34 apply (zenon_L20_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.13/10.34 apply (zenon_L21_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.13/10.34 apply (zenon_L22_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.13/10.34 apply (zenon_L23_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.13/10.34 apply (zenon_L24_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.13/10.34 apply (zenon_L25_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.13/10.34 apply (zenon_L26_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.13/10.34 apply (zenon_L27_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.13/10.34 apply (zenon_L30_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.13/10.34 apply (zenon_L31_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.13/10.34 apply (zenon_L32_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.13/10.34 apply (zenon_L129_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.13/10.34 apply (zenon_L55_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.13/10.34 apply (zenon_L56_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.13/10.34 apply (zenon_L229_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.13/10.34 apply (zenon_L147_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.13/10.34 apply (zenon_L148_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.13/10.34 apply (zenon_L230_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.13/10.34 apply (zenon_L150_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.13/10.34 apply (zenon_L206_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.13/10.34 apply (zenon_L207_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.13/10.34 apply (zenon_L154_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.13/10.34 apply (zenon_L155_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_Hc3. zenon_intro zenon_H1bf. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H163. zenon_intro zenon_H83. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.13/10.34 apply (zenon_L232_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.13/10.34 apply (zenon_L157_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.13/10.34 apply (zenon_L158_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.13/10.34 apply (zenon_L159_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.13/10.34 apply (zenon_L160_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.13/10.34 apply (zenon_L233_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_Hd4. zenon_intro zenon_H1d0. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_Hff. zenon_intro zenon_Hf2. % 10.13/10.34 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.13/10.34 apply (zenon_L29_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.13/10.34 apply (zenon_L235_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.13/10.34 apply (zenon_L239_); trivial. % 10.13/10.34 apply (zenon_L240_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.13/10.34 apply (zenon_L164_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.13/10.34 apply (zenon_L165_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.13/10.34 apply (zenon_L166_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.13/10.34 apply (zenon_L241_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.13/10.34 apply (zenon_L242_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.13/10.34 apply (zenon_L169_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.13/10.34 apply (zenon_L243_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.13/10.34 apply (zenon_L172_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H127. zenon_intro zenon_H1e7. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1e5. zenon_intro zenon_H80. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.13/10.34 apply (zenon_L244_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.13/10.34 apply (zenon_L187_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.13/10.34 apply (zenon_L245_); trivial. % 10.13/10.34 exact (zenon_H1e5 zenon_H189). % 10.13/10.34 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.13/10.34 apply (zenon_L174_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.13/10.34 apply (zenon_L246_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H1ed. zenon_intro zenon_H1f4. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1f4). zenon_intro zenon_H1ee. zenon_intro zenon_H8f. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.34 apply (zenon_L54_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.34 apply (zenon_L251_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.34 apply (zenon_L252_); trivial. % 10.13/10.34 apply (zenon_L254_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.13/10.34 apply (zenon_L178_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.13/10.34 apply (zenon_L179_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.13/10.34 apply (zenon_L180_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.13/10.34 apply (zenon_L181_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.13/10.34 apply (zenon_L182_); trivial. % 10.13/10.34 apply (zenon_L183_); trivial. % 10.13/10.34 apply (zenon_L277_); trivial. % 10.13/10.34 apply (zenon_L262_); trivial. % 10.13/10.34 (* end of lemma zenon_L278_ *) % 10.13/10.34 assert (zenon_L279_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H12a zenon_Hf6 zenon_H104 zenon_H36 zenon_Hfd zenon_Hc3 zenon_He9 zenon_H128. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.13/10.34 apply (zenon_L99_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.13/10.34 apply (zenon_L225_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.13/10.34 apply (zenon_L73_); trivial. % 10.13/10.34 apply (zenon_L77_); trivial. % 10.13/10.34 (* end of lemma zenon_L279_ *) % 10.13/10.34 assert (zenon_L280_ : ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H189 zenon_Hef zenon_H29d. % 10.13/10.34 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.13/10.34 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H29d. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_Hd6. % 10.13/10.34 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.34 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H29e]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H29e. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H189. % 10.13/10.34 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H29f]. % 10.13/10.34 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.34 congruence. % 10.13/10.34 apply zenon_Hd7. apply refl_equal. % 10.13/10.34 apply zenon_H29f. apply sym_equal. exact zenon_Hef. % 10.13/10.34 apply zenon_Hd7. apply refl_equal. % 10.13/10.34 apply zenon_Hd7. apply refl_equal. % 10.13/10.34 (* end of lemma zenon_L280_ *) % 10.13/10.34 assert (zenon_L281_ : ((op (e2) (e1)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_Hc3 zenon_Ha4 zenon_H100. % 10.13/10.34 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H1b4 ]. % 10.13/10.34 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e0) (e1)) = (op (e2) (e1)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H100. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H1b3. % 10.13/10.34 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 10.13/10.34 cut (((op (e2) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e0) (e1)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H2a0. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_Hc3. % 10.13/10.34 cut (((e2) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a1]. % 10.13/10.34 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 10.13/10.34 congruence. % 10.13/10.34 apply zenon_H1b4. apply refl_equal. % 10.13/10.34 apply zenon_H2a1. apply sym_equal. exact zenon_Ha4. % 10.13/10.34 apply zenon_H1b4. apply refl_equal. % 10.13/10.34 apply zenon_H1b4. apply refl_equal. % 10.13/10.34 (* end of lemma zenon_L281_ *) % 10.13/10.34 assert (zenon_L282_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H177 zenon_H6a zenon_H36. % 10.13/10.34 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H177. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H6a. % 10.13/10.34 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 10.13/10.34 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H270]. % 10.13/10.34 congruence. % 10.13/10.34 apply zenon_H270. apply refl_equal. % 10.13/10.34 apply zenon_Ha0. apply sym_equal. exact zenon_H36. % 10.13/10.34 (* end of lemma zenon_L282_ *) % 10.13/10.34 assert (zenon_L283_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H24e zenon_H104 zenon_H119 zenon_H6a zenon_H177 zenon_Hc3 zenon_Hf4 zenon_H128 zenon_H99. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.13/10.34 apply (zenon_L99_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.13/10.34 apply (zenon_L282_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.13/10.34 apply (zenon_L193_); trivial. % 10.13/10.34 apply (zenon_L111_); trivial. % 10.13/10.34 (* end of lemma zenon_L283_ *) % 10.13/10.34 assert (zenon_L284_ : ((op (e0) (e2)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H16e zenon_Hc7 zenon_Hfc. % 10.13/10.34 apply (zenon_notand_s _ _ ax22); [ zenon_intro zenon_H109 | zenon_intro zenon_H2a2 ]. % 10.13/10.34 apply zenon_H109. apply sym_equal. exact zenon_Hfc. % 10.13/10.34 apply (zenon_notand_s _ _ zenon_H2a2); [ zenon_intro zenon_H16c | zenon_intro zenon_H2a3 ]. % 10.13/10.34 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.13/10.34 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((e0) = (op (e2) (op (e2) (e2))))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H16c. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H10c. % 10.13/10.34 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.13/10.34 cut (((op (e2) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (op (e2) (e2))) = (e0))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H168. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_Hc7. % 10.13/10.34 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.34 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 10.13/10.34 congruence. % 10.13/10.34 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.13/10.34 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e3)) = (op (e2) (op (e2) (e2))))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H10f. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H10c. % 10.13/10.34 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.13/10.34 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 10.13/10.34 congruence. % 10.13/10.34 apply (zenon_L63_); trivial. % 10.13/10.34 apply zenon_H10d. apply refl_equal. % 10.13/10.34 apply zenon_H10d. apply refl_equal. % 10.13/10.34 apply zenon_H84. apply refl_equal. % 10.13/10.34 apply zenon_H10d. apply refl_equal. % 10.13/10.34 apply zenon_H10d. apply refl_equal. % 10.13/10.34 elim (classic ((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 10.13/10.34 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2))) = ((e1) = (op (op (e2) (op (e2) (e2))) (e2)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H2a3. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H110. % 10.13/10.34 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 10.13/10.34 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2a4]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((op (e0) (e2)) = (e1)) = ((op (op (e2) (op (e2) (e2))) (e2)) = (e1))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H2a4. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H16e. % 10.13/10.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.34 cut (((op (e0) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H166]. % 10.13/10.34 congruence. % 10.13/10.34 elim (classic ((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 10.13/10.34 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2))) = ((op (e0) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H166. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H110. % 10.13/10.34 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 10.13/10.34 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.34 cut (((op (e2) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (op (e2) (e2))) = (e0))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H168. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_Hc7. % 10.13/10.34 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.34 cut (((op (e2) (e3)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 10.13/10.34 congruence. % 10.13/10.34 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.13/10.34 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e3)) = (op (e2) (op (e2) (e2))))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H10f. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H10c. % 10.13/10.34 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.13/10.34 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 10.13/10.34 congruence. % 10.13/10.34 apply (zenon_L63_); trivial. % 10.13/10.34 apply zenon_H10d. apply refl_equal. % 10.13/10.34 apply zenon_H10d. apply refl_equal. % 10.13/10.34 apply zenon_H84. apply refl_equal. % 10.13/10.34 apply zenon_H87. apply refl_equal. % 10.13/10.34 apply zenon_H111. apply refl_equal. % 10.13/10.34 apply zenon_H111. apply refl_equal. % 10.13/10.34 apply zenon_H98. apply refl_equal. % 10.13/10.34 apply zenon_H111. apply refl_equal. % 10.13/10.34 apply zenon_H111. apply refl_equal. % 10.13/10.34 (* end of lemma zenon_L284_ *) % 10.13/10.34 assert (zenon_L285_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H15b zenon_H135 zenon_H13b zenon_H119 zenon_H100 zenon_H16e zenon_H266 zenon_Hc7 zenon_H115 zenon_H36 zenon_He5 zenon_H24b zenon_Hc6. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.13/10.34 apply (zenon_L211_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.13/10.34 apply (zenon_L212_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.13/10.34 apply (zenon_L284_); trivial. % 10.13/10.34 apply (zenon_L215_); trivial. % 10.13/10.34 (* end of lemma zenon_L285_ *) % 10.13/10.34 assert (zenon_L286_ : (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (e3)) = (e1)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H104 zenon_H67 zenon_H189. % 10.13/10.34 cut (((op (e3) (e3)) = (e3)) = ((e1) = (e3))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H104. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H67. % 10.13/10.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.34 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 10.13/10.34 congruence. % 10.13/10.34 exact (zenon_H1e5 zenon_H189). % 10.13/10.34 apply zenon_Heb. apply refl_equal. % 10.13/10.34 (* end of lemma zenon_L286_ *) % 10.13/10.34 assert (zenon_L287_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H2a5 zenon_Hc3 zenon_H51. % 10.13/10.34 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e2)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H2a5. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_Hc3. % 10.13/10.34 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a6]. % 10.13/10.34 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 10.13/10.34 congruence. % 10.13/10.34 apply zenon_H1b4. apply refl_equal. % 10.13/10.34 apply zenon_H2a6. apply sym_equal. exact zenon_H51. % 10.13/10.34 (* end of lemma zenon_L287_ *) % 10.13/10.34 assert (zenon_L288_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H1be zenon_H2a5 zenon_H51. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_Hc3. zenon_intro zenon_H1bf. % 10.13/10.34 apply (zenon_L287_); trivial. % 10.13/10.34 (* end of lemma zenon_L288_ *) % 10.13/10.34 assert (zenon_L289_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H278 zenon_Hfc zenon_H1ed. % 10.13/10.34 cut (((op (e2) (e2)) = (e3)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H278. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_Hfc. % 10.13/10.34 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a7]. % 10.13/10.34 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.34 congruence. % 10.13/10.34 apply zenon_Hd0. apply refl_equal. % 10.13/10.34 apply zenon_H2a7. apply sym_equal. exact zenon_H1ed. % 10.13/10.34 (* end of lemma zenon_L289_ *) % 10.13/10.34 assert (zenon_L290_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H2a8 zenon_H189 zenon_H104 zenon_H186 zenon_H1ea zenon_H15b zenon_H135 zenon_H119 zenon_H100 zenon_H266 zenon_H115 zenon_H36 zenon_He5 zenon_H24b zenon_Hc6 zenon_H244 zenon_Hc7 zenon_H16e zenon_H290 zenon_H71 zenon_H163 zenon_H2a5 zenon_H1be zenon_H278. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.13/10.34 apply (zenon_L105_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.13/10.34 apply (zenon_L285_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.13/10.34 exact (zenon_H1ea zenon_H127). % 10.13/10.34 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.13/10.34 apply (zenon_L249_); trivial. % 10.13/10.34 apply (zenon_L286_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.13/10.34 apply (zenon_L284_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H74 | zenon_intro zenon_H291 ]. % 10.13/10.34 exact (zenon_H71 zenon_H74). % 10.13/10.34 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H103 | zenon_intro zenon_H292 ]. % 10.13/10.34 exact (zenon_H163 zenon_H103). % 10.13/10.34 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfc ]. % 10.13/10.34 apply (zenon_L288_); trivial. % 10.13/10.34 apply (zenon_L289_); trivial. % 10.13/10.34 (* end of lemma zenon_L290_ *) % 10.13/10.34 assert (zenon_L291_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H12d zenon_H37 zenon_H6b zenon_H2ab zenon_H99 zenon_Hf4 zenon_H177 zenon_H24e zenon_H278 zenon_H1be zenon_H2a5 zenon_H163 zenon_H71 zenon_H290 zenon_H244 zenon_Hc6 zenon_H24b zenon_He5 zenon_H115 zenon_H266 zenon_H100 zenon_H119 zenon_H135 zenon_H15b zenon_H1ea zenon_H186 zenon_H104 zenon_H2a8 zenon_H85 zenon_Hc3 zenon_Hc0 zenon_H1f zenon_Hca zenon_Hda zenon_H16e zenon_H189 zenon_H29d. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.34 apply (zenon_L7_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.34 exact (zenon_H6b zenon_H6f). % 10.13/10.34 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.34 apply (zenon_L45_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.34 apply (zenon_L283_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.13/10.34 apply (zenon_L44_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.13/10.34 apply (zenon_L45_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.13/10.34 exact (zenon_H71 zenon_H74). % 10.13/10.34 apply (zenon_L290_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.34 apply (zenon_L131_); trivial. % 10.13/10.34 apply (zenon_L280_); trivial. % 10.13/10.34 (* end of lemma zenon_L291_ *) % 10.13/10.34 assert (zenon_L292_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H1cf zenon_H36 zenon_H104. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_Hd4. zenon_intro zenon_H1d0. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_Hff. zenon_intro zenon_Hf2. % 10.13/10.34 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.13/10.34 apply (zenon_L225_); trivial. % 10.13/10.34 (* end of lemma zenon_L292_ *) % 10.13/10.34 assert (zenon_L293_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H2ae zenon_H47 zenon_H1f zenon_H99 zenon_H71 zenon_H2a8 zenon_Hfd zenon_Hcd zenon_H104 zenon_H8b zenon_Hff zenon_He9. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.13/10.34 apply (zenon_L11_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.13/10.34 apply (zenon_L35_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.13/10.34 exact (zenon_H71 zenon_H74). % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.13/10.34 apply (zenon_L91_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.13/10.34 apply (zenon_L118_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.13/10.34 exact (zenon_Hff zenon_Hfc). % 10.13/10.34 apply (zenon_L185_); trivial. % 10.13/10.34 (* end of lemma zenon_L293_ *) % 10.13/10.34 assert (zenon_L294_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H2ab zenon_H29c zenon_H130 zenon_H1b2 zenon_H281 zenon_Hc0 zenon_H15b zenon_H298 zenon_He6 zenon_H269 zenon_H293 zenon_H28f zenon_H290 zenon_H287 zenon_H289 zenon_H1cb zenon_H1de zenon_H1ef zenon_H28c zenon_H284 zenon_Hca zenon_H171 zenon_H135 zenon_H37 zenon_H5b zenon_H85 zenon_H18d zenon_H138 zenon_H94 zenon_Hbb zenon_Hf4 zenon_Hd5 zenon_H124 zenon_H272 zenon_Hdf zenon_Hc6 zenon_Hda zenon_H157 zenon_H1a3 zenon_H13d zenon_H278 zenon_H18a zenon_Hb6 zenon_H186 zenon_H17e zenon_H27c zenon_H24b zenon_H15e zenon_H202 zenon_H29b zenon_H1cf zenon_He9 zenon_Hff zenon_H104 zenon_Hcd zenon_Hfd zenon_H2a8 zenon_H71 zenon_H99 zenon_H1f zenon_H47 zenon_H2ae zenon_Hf3. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.34 apply (zenon_L278_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.34 apply (zenon_L292_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.34 apply (zenon_L293_); trivial. % 10.13/10.34 exact (zenon_Hf3 zenon_Hef). % 10.13/10.34 (* end of lemma zenon_L294_ *) % 10.13/10.34 assert (zenon_L295_ : ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H31 zenon_H5a zenon_H104. % 10.13/10.34 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.34 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H104. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_Hea. % 10.13/10.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.34 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((op (e0) (e0)) = (e1)) = ((e3) = (e1))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H105. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H31. % 10.13/10.34 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.34 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 10.13/10.34 congruence. % 10.13/10.34 exact (zenon_H58 zenon_H5a). % 10.13/10.34 apply zenon_H98. apply refl_equal. % 10.13/10.34 apply zenon_Heb. apply refl_equal. % 10.13/10.34 apply zenon_Heb. apply refl_equal. % 10.13/10.34 (* end of lemma zenon_L295_ *) % 10.13/10.34 assert (zenon_L296_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H18a zenon_H31 zenon_H130 zenon_H127 zenon_H104 zenon_H8b zenon_H186 zenon_H1e5. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.13/10.34 apply (zenon_L82_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.13/10.34 apply (zenon_L187_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.13/10.34 apply (zenon_L125_); trivial. % 10.13/10.34 exact (zenon_H1e5 zenon_H189). % 10.13/10.34 (* end of lemma zenon_L296_ *) % 10.13/10.34 assert (zenon_L297_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H1e1 zenon_H18a zenon_H130 zenon_H104 zenon_H8b zenon_H186. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H127. zenon_intro zenon_H1e2. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H1e5. zenon_intro zenon_H2e. % 10.13/10.34 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.13/10.34 apply (zenon_L296_); trivial. % 10.13/10.34 (* end of lemma zenon_L297_ *) % 10.13/10.34 assert (zenon_L298_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H278 zenon_H74 zenon_H241. % 10.13/10.34 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H278. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H74. % 10.13/10.34 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2b1]. % 10.13/10.34 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.34 congruence. % 10.13/10.34 apply zenon_Hd0. apply refl_equal. % 10.13/10.34 apply zenon_H2b1. apply sym_equal. exact zenon_H241. % 10.13/10.34 (* end of lemma zenon_L298_ *) % 10.13/10.34 assert (zenon_L299_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H287 zenon_Hb9 zenon_H51. % 10.13/10.34 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H287. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_Hb9. % 10.13/10.34 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a6]. % 10.13/10.34 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 10.13/10.34 congruence. % 10.13/10.34 apply zenon_Hbd. apply refl_equal. % 10.13/10.34 apply zenon_H2a6. apply sym_equal. exact zenon_H51. % 10.13/10.34 (* end of lemma zenon_L299_ *) % 10.13/10.34 assert (zenon_L300_ : ((op (e2) (e0)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((e3) = (op (op (e0) (op (e0) (e0))) (e0)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H152 zenon_Ha4 zenon_H31 zenon_H2b2. % 10.13/10.34 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.13/10.34 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((e3) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H2b2. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H256. % 10.13/10.34 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.13/10.34 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2b3]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((op (e2) (e0)) = (e3)) = ((op (op (e0) (op (e0) (e0))) (e0)) = (e3))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H2b3. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H152. % 10.13/10.34 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.34 cut (((op (e2) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b4]. % 10.13/10.34 congruence. % 10.13/10.34 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.13/10.34 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((op (e2) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H2b4. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H256. % 10.13/10.34 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.13/10.34 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b5]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.34 cut (((op (e0) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2b6]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (op (e0) (e0))) = (e2))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H2b6. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_Ha4. % 10.13/10.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.34 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25c]. % 10.13/10.34 congruence. % 10.13/10.34 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.13/10.34 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e1)) = (op (e0) (op (e0) (e0))))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H25c. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H25d. % 10.13/10.34 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.13/10.34 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H254]. % 10.13/10.34 congruence. % 10.13/10.34 apply (zenon_L200_); trivial. % 10.13/10.34 apply zenon_H25e. apply refl_equal. % 10.13/10.34 apply zenon_H25e. apply refl_equal. % 10.13/10.34 apply zenon_H87. apply refl_equal. % 10.13/10.34 apply zenon_H84. apply refl_equal. % 10.13/10.34 apply zenon_H257. apply refl_equal. % 10.13/10.34 apply zenon_H257. apply refl_equal. % 10.13/10.34 apply zenon_Heb. apply refl_equal. % 10.13/10.34 apply zenon_H257. apply refl_equal. % 10.13/10.34 apply zenon_H257. apply refl_equal. % 10.13/10.34 (* end of lemma zenon_L300_ *) % 10.13/10.34 assert (zenon_L301_ : ((op (e2) (e0)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H152 zenon_Ha4 zenon_H31. % 10.13/10.34 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H260 | zenon_intro zenon_H2b7 ]. % 10.13/10.34 apply zenon_H260. apply sym_equal. exact zenon_H31. % 10.13/10.34 apply (zenon_notand_s _ _ zenon_H2b7); [ zenon_intro zenon_H2b8 | zenon_intro zenon_H2b2 ]. % 10.13/10.34 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.13/10.34 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e2) = (op (e0) (op (e0) (e0))))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H2b8. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H25d. % 10.13/10.34 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.13/10.34 cut (((op (e0) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2b6]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (op (e0) (e0))) = (e2))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H2b6. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_Ha4. % 10.13/10.34 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.34 cut (((op (e0) (e1)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25c]. % 10.13/10.34 congruence. % 10.13/10.34 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.13/10.34 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e1)) = (op (e0) (op (e0) (e0))))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H25c. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H25d. % 10.13/10.34 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.13/10.34 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H254]. % 10.13/10.34 congruence. % 10.13/10.34 apply (zenon_L200_); trivial. % 10.13/10.34 apply zenon_H25e. apply refl_equal. % 10.13/10.34 apply zenon_H25e. apply refl_equal. % 10.13/10.34 apply zenon_H87. apply refl_equal. % 10.13/10.34 apply zenon_H25e. apply refl_equal. % 10.13/10.34 apply zenon_H25e. apply refl_equal. % 10.13/10.34 apply (zenon_L300_); trivial. % 10.13/10.34 (* end of lemma zenon_L301_ *) % 10.13/10.34 assert (zenon_L302_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H28c zenon_Hc4 zenon_H1b2 zenon_Hc0 zenon_H51 zenon_H287 zenon_Ha4 zenon_H31. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H28d ]. % 10.13/10.34 apply (zenon_L259_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_Hfa | zenon_intro zenon_H28e ]. % 10.13/10.34 apply (zenon_L121_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H152 ]. % 10.13/10.34 apply (zenon_L299_); trivial. % 10.13/10.34 apply (zenon_L301_); trivial. % 10.13/10.34 (* end of lemma zenon_L302_ *) % 10.13/10.34 assert (zenon_L303_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H245 zenon_H1f zenon_H130 zenon_H127 zenon_He9 zenon_H107 zenon_H9a zenon_H28c zenon_Hc4 zenon_H1b2 zenon_Hc0 zenon_H287 zenon_Ha4 zenon_H31 zenon_H278 zenon_H187 zenon_H290 zenon_H76. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.13/10.34 apply (zenon_L81_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.13/10.34 apply (zenon_L77_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H74 | zenon_intro zenon_H291 ]. % 10.13/10.34 apply (zenon_L298_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H103 | zenon_intro zenon_H292 ]. % 10.13/10.34 apply (zenon_L245_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfc ]. % 10.13/10.34 apply (zenon_L302_); trivial. % 10.13/10.34 apply (zenon_L64_); trivial. % 10.13/10.34 exact (zenon_H76 zenon_H79). % 10.13/10.34 (* end of lemma zenon_L303_ *) % 10.13/10.34 assert (zenon_L304_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H293 zenon_H186 zenon_H104 zenon_H18a zenon_H1e1 zenon_H150 zenon_H245 zenon_H1f zenon_H130 zenon_H127 zenon_He9 zenon_H107 zenon_H9a zenon_H28c zenon_Hc4 zenon_H1b2 zenon_Hc0 zenon_H287 zenon_Ha4 zenon_H31 zenon_H278 zenon_H290 zenon_H76. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.13/10.34 apply (zenon_L105_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.13/10.34 apply (zenon_L297_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.13/10.34 apply (zenon_L102_); trivial. % 10.13/10.34 apply (zenon_L303_); trivial. % 10.13/10.34 (* end of lemma zenon_L304_ *) % 10.13/10.34 assert (zenon_L305_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H272 zenon_H5b zenon_H1f zenon_Hef zenon_H99 zenon_Hd4 zenon_H85 zenon_H76. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.13/10.34 apply (zenon_L16_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.13/10.34 apply (zenon_L71_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.13/10.34 apply (zenon_L234_); trivial. % 10.13/10.34 exact (zenon_H76 zenon_H79). % 10.13/10.34 (* end of lemma zenon_L305_ *) % 10.13/10.34 assert (zenon_L306_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.13/10.34 do 0 intro. intros zenon_H12d zenon_H30 zenon_H6b zenon_H13d zenon_Hb9 zenon_Hbb zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H135 zenon_H130 zenon_H31 zenon_H145 zenon_H99 zenon_H9a zenon_H124 zenon_Hf4 zenon_H171 zenon_H293 zenon_H186 zenon_H104 zenon_H18a zenon_H1e1 zenon_H150 zenon_H245 zenon_H28c zenon_H1b2 zenon_Hc0 zenon_H287 zenon_Ha4 zenon_H278 zenon_H290 zenon_H76 zenon_H289 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H18d zenon_H1cb zenon_H1de zenon_H1ef zenon_H2ab zenon_He9 zenon_H127. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.34 exact (zenon_H30 zenon_H2d). % 10.13/10.34 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.34 exact (zenon_H6b zenon_H6f). % 10.13/10.34 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.34 apply (zenon_L262_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.34 apply (zenon_L59_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.34 apply (zenon_L107_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.34 apply (zenon_L102_); trivial. % 10.13/10.34 apply (zenon_L304_); trivial. % 10.13/10.34 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.34 apply (zenon_L35_); trivial. % 10.13/10.34 apply (zenon_L87_); trivial. % 10.13/10.34 apply (zenon_L77_); trivial. % 10.13/10.34 (* end of lemma zenon_L306_ *) % 10.13/10.34 assert (zenon_L307_ : ((op (e2) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.13/10.34 do 0 intro. intros zenon_H51 zenon_Hdb zenon_H182. % 10.13/10.34 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd0 ]. % 10.13/10.34 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H182. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_Hcf. % 10.13/10.34 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.34 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 10.13/10.34 congruence. % 10.13/10.34 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_H183. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H51. % 10.13/10.34 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 10.13/10.34 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.34 congruence. % 10.13/10.34 apply zenon_Hd0. apply refl_equal. % 10.13/10.34 apply zenon_Hdc. apply sym_equal. exact zenon_Hdb. % 10.13/10.34 apply zenon_Hd0. apply refl_equal. % 10.13/10.34 apply zenon_Hd0. apply refl_equal. % 10.13/10.34 (* end of lemma zenon_L307_ *) % 10.13/10.34 assert (zenon_L308_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> False). % 10.13/10.34 do 0 intro. intros zenon_Hda zenon_H150 zenon_H17a. % 10.13/10.34 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 10.13/10.34 intro zenon_D_pnotp. % 10.13/10.34 apply zenon_Hda. % 10.13/10.34 rewrite <- zenon_D_pnotp. % 10.13/10.34 exact zenon_H150. % 10.13/10.34 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 10.13/10.34 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 10.13/10.34 congruence. % 10.13/10.34 apply zenon_H49. apply refl_equal. % 10.13/10.34 apply zenon_H27b. apply sym_equal. exact zenon_H17a. % 10.13/10.34 (* end of lemma zenon_L308_ *) % 10.13/10.34 assert (zenon_L309_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H17e zenon_H13d zenon_H13b zenon_Ha4 zenon_H150 zenon_Hda zenon_Ha5 zenon_He9. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.35 apply (zenon_L85_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.35 apply (zenon_L40_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.35 apply (zenon_L308_); trivial. % 10.13/10.35 apply (zenon_L119_); trivial. % 10.13/10.35 (* end of lemma zenon_L309_ *) % 10.13/10.35 assert (zenon_L310_ : (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> False). % 10.13/10.35 do 0 intro. intros zenon_Hf4 zenon_H91 zenon_H36. % 10.13/10.35 cut (((op (e1) (e1)) = (e2)) = ((e1) = (e2))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_Hf4. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_H91. % 10.13/10.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.35 cut (((op (e1) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 10.13/10.35 congruence. % 10.13/10.35 exact (zenon_H35 zenon_H36). % 10.13/10.35 apply zenon_H87. apply refl_equal. % 10.13/10.35 (* end of lemma zenon_L310_ *) % 10.13/10.35 assert (zenon_L311_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H2b9 zenon_He9 zenon_Ha5 zenon_Hda zenon_H150 zenon_H13d zenon_H17e zenon_H135 zenon_Hb9 zenon_H130 zenon_H31 zenon_H1f zenon_H145 zenon_H36 zenon_Hf4 zenon_Hc4 zenon_H85 zenon_Hfd zenon_H127. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H131 | zenon_intro zenon_H146 ]. % 10.13/10.35 apply (zenon_L81_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H133 | zenon_intro zenon_H147 ]. % 10.13/10.35 apply (zenon_L82_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H136 | zenon_intro zenon_H13b ]. % 10.13/10.35 apply (zenon_L83_); trivial. % 10.13/10.35 apply (zenon_L309_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.13/10.35 apply (zenon_L310_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.13/10.35 apply (zenon_L45_); trivial. % 10.13/10.35 apply (zenon_L199_); trivial. % 10.13/10.35 (* end of lemma zenon_L311_ *) % 10.13/10.35 assert (zenon_L312_ : ((op (e1) (e1)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H6f zenon_H36 zenon_H99. % 10.13/10.35 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H98 ]. % 10.13/10.35 cut (((e1) = (e1)) = ((e0) = (e1))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_H99. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_Hf7. % 10.13/10.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.35 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 10.13/10.35 congruence. % 10.13/10.35 cut (((op (e1) (e1)) = (e0)) = ((e1) = (e0))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_Hf8. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_H6f. % 10.13/10.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.35 cut (((op (e1) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 10.13/10.35 congruence. % 10.13/10.35 exact (zenon_H35 zenon_H36). % 10.13/10.35 apply zenon_H84. apply refl_equal. % 10.13/10.35 apply zenon_H98. apply refl_equal. % 10.13/10.35 apply zenon_H98. apply refl_equal. % 10.13/10.35 (* end of lemma zenon_L312_ *) % 10.13/10.35 assert (zenon_L313_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H12d zenon_H30 zenon_Ha5 zenon_H99 zenon_H18a zenon_H130 zenon_H104 zenon_H186 zenon_H1e5 zenon_H13c zenon_H2ab zenon_H31 zenon_Ha4 zenon_H287 zenon_H51 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_He9 zenon_H127. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.35 exact (zenon_H30 zenon_H2d). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.35 apply (zenon_L248_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.35 apply (zenon_L312_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.35 apply (zenon_L296_); trivial. % 10.13/10.35 apply (zenon_L71_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.35 apply (zenon_L302_); trivial. % 10.13/10.35 apply (zenon_L77_); trivial. % 10.13/10.35 (* end of lemma zenon_L313_ *) % 10.13/10.35 assert (zenon_L314_ : (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H6b zenon_Ha5 zenon_H99 zenon_H1e1 zenon_H18a zenon_H130 zenon_H104 zenon_H186 zenon_H12d zenon_H30 zenon_H1e5 zenon_H13c zenon_H2ab zenon_H31 zenon_H287 zenon_H1b2 zenon_H28c zenon_H2b9 zenon_Hda zenon_H150 zenon_H13d zenon_H17e zenon_H135 zenon_H145 zenon_He0 zenon_H171 zenon_H124 zenon_Hf4 zenon_Hc6 zenon_H71 zenon_H85 zenon_Hc0 zenon_H1f zenon_Hca zenon_Hfd zenon_H94 zenon_He9 zenon_H127. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.35 exact (zenon_H30 zenon_H2d). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.35 exact (zenon_H6b zenon_H6f). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.35 apply (zenon_L243_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.35 apply (zenon_L121_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.35 apply (zenon_L107_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.35 apply (zenon_L102_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.35 apply (zenon_L311_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.35 apply (zenon_L45_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.35 apply (zenon_L313_); trivial. % 10.13/10.35 apply (zenon_L269_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.13/10.35 apply (zenon_L310_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.13/10.35 apply (zenon_L47_); trivial. % 10.13/10.35 apply (zenon_L199_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.35 apply (zenon_L297_); trivial. % 10.13/10.35 apply (zenon_L71_); trivial. % 10.13/10.35 apply (zenon_L77_); trivial. % 10.13/10.35 (* end of lemma zenon_L314_ *) % 10.13/10.35 assert (zenon_L315_ : ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H127 zenon_He9 zenon_H94 zenon_Hfd zenon_Hca zenon_H1f zenon_Hc0 zenon_H85 zenon_H71 zenon_Hc6 zenon_Hf4 zenon_H124 zenon_H171 zenon_He0 zenon_H145 zenon_H135 zenon_H17e zenon_H13d zenon_H150 zenon_Hda zenon_H2b9 zenon_H28c zenon_H1b2 zenon_H287 zenon_H2ab zenon_H1e5 zenon_H30 zenon_H12d zenon_H186 zenon_H104 zenon_H130 zenon_H18a zenon_H99 zenon_H6b zenon_Hdf zenon_H100 zenon_H173 zenon_H76 zenon_H5b zenon_H272 zenon_H182 zenon_Hbb zenon_H138 zenon_H142 zenon_H293 zenon_H245 zenon_H278 zenon_H290 zenon_H289 zenon_H202 zenon_H37 zenon_H47 zenon_H18d zenon_H1cb zenon_H1ef zenon_H115 zenon_H24e zenon_Hb6 zenon_H31 zenon_Ha4 zenon_H1e1 zenon_H1de. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.13/10.35 apply (zenon_L54_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.35 apply (zenon_L33_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.35 exact (zenon_H6b zenon_H6f). % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.35 exact (zenon_H30 zenon_H2d). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.35 exact (zenon_H6b zenon_H6f). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.35 apply (zenon_L243_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.35 apply (zenon_L121_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.35 apply (zenon_L107_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.35 apply (zenon_L102_); trivial. % 10.13/10.35 apply (zenon_L304_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.35 apply (zenon_L296_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.13/10.35 apply (zenon_L89_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.13/10.35 apply (zenon_L65_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.35 apply (zenon_L43_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.35 apply (zenon_L281_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.35 apply (zenon_L302_); trivial. % 10.13/10.35 apply (zenon_L305_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.13/10.35 apply (zenon_L108_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.35 apply (zenon_L306_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.35 apply (zenon_L193_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.35 apply (zenon_L307_); trivial. % 10.13/10.35 apply (zenon_L305_); trivial. % 10.13/10.35 apply (zenon_L97_); trivial. % 10.13/10.35 apply (zenon_L187_); trivial. % 10.13/10.35 apply (zenon_L77_); trivial. % 10.13/10.35 apply (zenon_L314_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.13/10.35 apply (zenon_L301_); trivial. % 10.13/10.35 apply (zenon_L171_); trivial. % 10.13/10.35 (* end of lemma zenon_L315_ *) % 10.13/10.35 assert (zenon_L316_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H12d zenon_H30 zenon_H6b zenon_Ha5 zenon_H99 zenon_H1e1 zenon_H18a zenon_H130 zenon_H104 zenon_H186 zenon_H2b9 zenon_Hda zenon_H150 zenon_H13d zenon_H17e zenon_H135 zenon_Hb9 zenon_H31 zenon_H1f zenon_H145 zenon_Hf4 zenon_H85 zenon_Hfd zenon_H94 zenon_H2ab zenon_He9 zenon_H127. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.35 exact (zenon_H30 zenon_H2d). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.35 exact (zenon_H6b zenon_H6f). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.35 apply (zenon_L243_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.35 apply (zenon_L311_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.35 apply (zenon_L297_); trivial. % 10.13/10.35 apply (zenon_L71_); trivial. % 10.13/10.35 apply (zenon_L77_); trivial. % 10.13/10.35 (* end of lemma zenon_L316_ *) % 10.13/10.35 assert (zenon_L317_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H15b zenon_Hfd zenon_Hb9 zenon_H154 zenon_H127 zenon_H107 zenon_H9a zenon_H157 zenon_H158. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.13/10.35 apply (zenon_L92_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.13/10.35 apply (zenon_L93_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.13/10.35 apply (zenon_L64_); trivial. % 10.13/10.35 apply (zenon_L94_); trivial. % 10.13/10.35 (* end of lemma zenon_L317_ *) % 10.13/10.35 assert (zenon_L318_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H2ab zenon_H1ef zenon_H1de zenon_H1cb zenon_H1b2 zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_He9 zenon_H289 zenon_H158 zenon_H157 zenon_H127 zenon_H154 zenon_Hfd zenon_H15b zenon_H104 zenon_H171 zenon_Hc0 zenon_H124 zenon_H9a zenon_H99 zenon_H145 zenon_H31 zenon_H130 zenon_H135 zenon_H142 zenon_H1f zenon_H94 zenon_H138 zenon_Hbb zenon_Hb9 zenon_H13d. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.35 apply (zenon_L262_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.35 apply (zenon_L121_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.35 apply (zenon_L107_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.35 apply (zenon_L95_); trivial. % 10.13/10.35 apply (zenon_L317_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.35 apply (zenon_L35_); trivial. % 10.13/10.35 apply (zenon_L87_); trivial. % 10.13/10.35 (* end of lemma zenon_L318_ *) % 10.13/10.35 assert (zenon_L319_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H74 zenon_Hfc zenon_He9. % 10.13/10.35 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.35 cut (((e3) = (e3)) = ((e0) = (e3))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_He9. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_Hea. % 10.13/10.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.35 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 10.13/10.35 congruence. % 10.13/10.35 cut (((op (e2) (e2)) = (e0)) = ((e3) = (e0))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_Hec. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_H74. % 10.13/10.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.35 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 10.13/10.35 congruence. % 10.13/10.35 exact (zenon_Hff zenon_Hfc). % 10.13/10.35 apply zenon_H84. apply refl_equal. % 10.13/10.35 apply zenon_Heb. apply refl_equal. % 10.13/10.35 apply zenon_Heb. apply refl_equal. % 10.13/10.35 (* end of lemma zenon_L319_ *) % 10.13/10.35 assert (zenon_L320_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e3) (e2)) = (e1)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H27c zenon_H16e zenon_H187. % 10.13/10.35 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_H27c. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_H16e. % 10.13/10.35 cut (((e1) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 10.13/10.35 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 10.13/10.35 congruence. % 10.13/10.35 apply zenon_H49. apply refl_equal. % 10.13/10.35 apply zenon_H188. apply sym_equal. exact zenon_H187. % 10.13/10.35 (* end of lemma zenon_L320_ *) % 10.13/10.35 assert (zenon_L321_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H18a zenon_H31 zenon_H130 zenon_H36 zenon_H262 zenon_H16e zenon_H27c zenon_H1e5. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.13/10.35 apply (zenon_L82_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.13/10.35 apply (zenon_L208_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.13/10.35 apply (zenon_L320_); trivial. % 10.13/10.35 exact (zenon_H1e5 zenon_H189). % 10.13/10.35 (* end of lemma zenon_L321_ *) % 10.13/10.35 assert (zenon_L322_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 10.13/10.35 do 0 intro. intros zenon_H27c zenon_H42 zenon_H241. % 10.13/10.35 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_H27c. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_H42. % 10.13/10.35 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2b1]. % 10.13/10.35 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 10.13/10.35 congruence. % 10.13/10.35 apply zenon_H49. apply refl_equal. % 10.13/10.35 apply zenon_H2b1. apply sym_equal. exact zenon_H241. % 10.13/10.35 (* end of lemma zenon_L322_ *) % 10.13/10.35 assert (zenon_L323_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H15e zenon_H14b zenon_H245 zenon_H28c zenon_H287 zenon_H278 zenon_H290 zenon_H76 zenon_H127 zenon_He9 zenon_H85 zenon_H2ae zenon_Hbb zenon_H138 zenon_H94 zenon_H142 zenon_H124 zenon_Hc0 zenon_H171 zenon_H289 zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H18d zenon_H1b2 zenon_H1cb zenon_H1ef zenon_H2ab zenon_H293 zenon_H262 zenon_H157 zenon_H154 zenon_H15b zenon_H2bc zenon_H27c zenon_H2b9 zenon_Hda zenon_H13d zenon_H17e zenon_H135 zenon_Hb9 zenon_H1f zenon_H145 zenon_Hf4 zenon_Hfd zenon_Hdf zenon_H1e5 zenon_H186 zenon_H104 zenon_H130 zenon_H18a zenon_H99 zenon_H6b zenon_H30 zenon_H12d zenon_Hb6 zenon_H31 zenon_Ha4 zenon_H1e1 zenon_H1de. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.35 apply (zenon_L54_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.35 apply (zenon_L90_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.35 apply (zenon_L33_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.35 exact (zenon_H6b zenon_H6f). % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.35 apply (zenon_L306_); trivial. % 10.13/10.35 apply (zenon_L316_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.13/10.35 apply (zenon_L295_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.35 apply (zenon_L33_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.35 exact (zenon_H6b zenon_H6f). % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.35 apply (zenon_L318_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.35 exact (zenon_H30 zenon_H2d). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.35 exact (zenon_H6b zenon_H6f). % 10.13/10.35 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.35 apply (zenon_L248_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.13/10.35 apply (zenon_L43_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.13/10.35 apply (zenon_L310_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.13/10.35 apply (zenon_L11_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.13/10.35 apply (zenon_L318_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.13/10.35 apply (zenon_L92_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.13/10.35 apply (zenon_L93_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.13/10.35 apply (zenon_L319_); trivial. % 10.13/10.35 apply (zenon_L94_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.13/10.35 apply (zenon_L321_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.13/10.35 apply (zenon_L297_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.13/10.35 apply (zenon_L95_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H42 | zenon_intro zenon_H2bd ]. % 10.13/10.35 apply (zenon_L322_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H16e | zenon_intro zenon_H2be ]. % 10.13/10.35 apply (zenon_L320_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_Hcd | zenon_intro zenon_H150 ]. % 10.13/10.35 apply (zenon_L50_); trivial. % 10.13/10.35 apply (zenon_L311_); trivial. % 10.13/10.35 apply (zenon_L51_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.35 apply (zenon_L296_); trivial. % 10.13/10.35 apply (zenon_L71_); trivial. % 10.13/10.35 apply (zenon_L77_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.13/10.35 apply (zenon_L301_); trivial. % 10.13/10.35 apply (zenon_L171_); trivial. % 10.13/10.35 (* end of lemma zenon_L323_ *) % 10.13/10.35 assert (zenon_L324_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H56 zenon_H158 zenon_He9. % 10.13/10.35 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.35 cut (((e3) = (e3)) = ((e0) = (e3))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_He9. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_Hea. % 10.13/10.35 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.35 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 10.13/10.35 congruence. % 10.13/10.35 cut (((op (e0) (e3)) = (e0)) = ((e3) = (e0))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_Hec. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_H56. % 10.13/10.35 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.35 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 10.13/10.35 congruence. % 10.13/10.35 exact (zenon_H16d zenon_H158). % 10.13/10.35 apply zenon_H84. apply refl_equal. % 10.13/10.35 apply zenon_Heb. apply refl_equal. % 10.13/10.35 apply zenon_Heb. apply refl_equal. % 10.13/10.35 (* end of lemma zenon_L324_ *) % 10.13/10.35 assert (zenon_L325_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H298 zenon_H104 zenon_H158 zenon_Ha5 zenon_H99 zenon_Hd4 zenon_Hf4 zenon_H1e5. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.13/10.35 apply (zenon_L135_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.13/10.35 apply (zenon_L71_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.13/10.35 apply (zenon_L269_); trivial. % 10.13/10.35 exact (zenon_H1e5 zenon_H189). % 10.13/10.35 (* end of lemma zenon_L325_ *) % 10.13/10.35 assert (zenon_L326_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H272 zenon_He9 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_H158 zenon_H104 zenon_H298 zenon_Hd4 zenon_H85 zenon_H76. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.13/10.35 apply (zenon_L324_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.13/10.35 apply (zenon_L325_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.13/10.35 apply (zenon_L234_); trivial. % 10.13/10.35 exact (zenon_H76 zenon_H79). % 10.13/10.35 (* end of lemma zenon_L326_ *) % 10.13/10.35 assert (zenon_L327_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((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 (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.35 do 0 intro. intros zenon_He0 zenon_H1de zenon_H1e1 zenon_Hb6 zenon_H12d zenon_H30 zenon_H6b zenon_H18a zenon_H130 zenon_H186 zenon_Hdf zenon_Hfd zenon_H145 zenon_H1f zenon_H135 zenon_H17e zenon_H13d zenon_Hda zenon_H2b9 zenon_H27c zenon_H2bc zenon_H15b zenon_H154 zenon_H157 zenon_H262 zenon_H293 zenon_H2ab zenon_H1ef zenon_H1cb zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_H289 zenon_H171 zenon_H124 zenon_H142 zenon_H94 zenon_H138 zenon_Hbb zenon_H2ae zenon_H127 zenon_H290 zenon_H278 zenon_H245 zenon_H14b zenon_H15e zenon_H101 zenon_H31 zenon_Ha4 zenon_H287 zenon_Hc0 zenon_H1b2 zenon_Hc4 zenon_H28c zenon_H272 zenon_He9 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_H158 zenon_H104 zenon_H298 zenon_H85 zenon_H76. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.35 apply (zenon_L323_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.35 apply (zenon_L193_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.35 apply (zenon_L302_); trivial. % 10.13/10.35 apply (zenon_L326_); trivial. % 10.13/10.35 (* end of lemma zenon_L327_ *) % 10.13/10.35 assert (zenon_L328_ : ((op (e2) (e2)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H103 zenon_H51 zenon_Hf4. % 10.13/10.35 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.13/10.35 cut (((e2) = (e2)) = ((e1) = (e2))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_Hf4. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_H86. % 10.13/10.35 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.35 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 10.13/10.35 congruence. % 10.13/10.35 cut (((op (e2) (e2)) = (e1)) = ((e2) = (e1))). % 10.13/10.35 intro zenon_D_pnotp. % 10.13/10.35 apply zenon_Hf5. % 10.13/10.35 rewrite <- zenon_D_pnotp. % 10.13/10.35 exact zenon_H103. % 10.13/10.35 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.35 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 10.13/10.35 congruence. % 10.13/10.35 exact (zenon_H50 zenon_H51). % 10.13/10.35 apply zenon_H98. apply refl_equal. % 10.13/10.35 apply zenon_H87. apply refl_equal. % 10.13/10.35 apply zenon_H87. apply refl_equal. % 10.13/10.35 (* end of lemma zenon_L328_ *) % 10.13/10.35 assert (zenon_L329_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.35 do 0 intro. intros zenon_He0 zenon_H157 zenon_H127 zenon_H154 zenon_Hfd zenon_H15b zenon_Hc4 zenon_H103 zenon_H272 zenon_He9 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_H158 zenon_H104 zenon_H298 zenon_H85 zenon_H76. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.35 apply (zenon_L95_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.35 apply (zenon_L45_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.35 apply (zenon_L328_); trivial. % 10.13/10.35 apply (zenon_L326_); trivial. % 10.13/10.35 (* end of lemma zenon_L329_ *) % 10.13/10.35 assert (zenon_L330_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.35 do 0 intro. intros zenon_H15e zenon_H14b zenon_H2ae zenon_Hbb zenon_H138 zenon_H94 zenon_H142 zenon_H124 zenon_H171 zenon_H289 zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H18d zenon_H1cb zenon_H1ef zenon_H2ab zenon_H2bc zenon_H2b9 zenon_Hda zenon_H13d zenon_H17e zenon_H135 zenon_H145 zenon_Hdf zenon_H6b zenon_H30 zenon_H12d zenon_Hb6 zenon_H1e1 zenon_H1de zenon_H293 zenon_H27c zenon_H262 zenon_H36 zenon_H186 zenon_H18a zenon_H85 zenon_H298 zenon_H104 zenon_H158 zenon_H99 zenon_Hf4 zenon_H1e5 zenon_H272 zenon_H15b zenon_Hfd zenon_H154 zenon_H157 zenon_He0 zenon_H245 zenon_H1f zenon_H130 zenon_H127 zenon_He9 zenon_H9a zenon_H28c zenon_Hc4 zenon_H1b2 zenon_Hc0 zenon_H287 zenon_Ha4 zenon_H31 zenon_H278 zenon_H290 zenon_H76. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.35 apply (zenon_L121_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.35 apply (zenon_L327_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.35 apply (zenon_L329_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.13/10.35 apply (zenon_L321_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.13/10.35 apply (zenon_L296_); trivial. % 10.13/10.35 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.13/10.35 apply (zenon_L329_); trivial. % 10.13/10.35 apply (zenon_L303_); trivial. % 10.13/10.35 (* end of lemma zenon_L330_ *) % 10.13/10.35 assert (zenon_L331_ : ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((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 (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H36 zenon_H298 zenon_H158 zenon_H272 zenon_He0 zenon_H1de zenon_H1e1 zenon_Hb6 zenon_H12d zenon_H30 zenon_H6b zenon_H99 zenon_H18a zenon_H130 zenon_H104 zenon_H186 zenon_H1e5 zenon_Hdf zenon_Hfd zenon_H145 zenon_H135 zenon_H17e zenon_H13d zenon_Hda zenon_H2b9 zenon_H27c zenon_H2bc zenon_H15b zenon_H154 zenon_H157 zenon_H262 zenon_H293 zenon_H2ab zenon_H1ef zenon_H1cb zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_H289 zenon_H171 zenon_H124 zenon_H142 zenon_H94 zenon_H138 zenon_Hbb zenon_H2ae zenon_He9 zenon_H127 zenon_H76 zenon_H290 zenon_H278 zenon_H245 zenon_H14b zenon_H15e zenon_Ha5 zenon_Hc6 zenon_H71 zenon_H85 zenon_H1f zenon_Hca zenon_H31 zenon_Ha4 zenon_H287 zenon_Hc0 zenon_H1b2 zenon_Hc4 zenon_H28c zenon_Hf4. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.36 apply (zenon_L121_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.36 apply (zenon_L107_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.36 apply (zenon_L329_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.36 apply (zenon_L323_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.36 apply (zenon_L47_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.36 apply (zenon_L302_); trivial. % 10.13/10.36 apply (zenon_L269_); trivial. % 10.13/10.36 (* end of lemma zenon_L331_ *) % 10.13/10.36 assert (zenon_L332_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.13/10.36 do 0 intro. intros zenon_H24e zenon_H99 zenon_H1e1 zenon_H18a zenon_H130 zenon_H104 zenon_H186 zenon_H298 zenon_H158 zenon_H272 zenon_He0 zenon_H1de zenon_Hb6 zenon_H12d zenon_H30 zenon_H6b zenon_H1e5 zenon_Hdf zenon_Hfd zenon_H145 zenon_H135 zenon_H17e zenon_H13d zenon_Hda zenon_H2b9 zenon_H27c zenon_H2bc zenon_H15b zenon_H154 zenon_H157 zenon_H262 zenon_H293 zenon_H2ab zenon_H1ef zenon_H1cb zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_H289 zenon_H171 zenon_H124 zenon_H142 zenon_H94 zenon_H138 zenon_Hbb zenon_H2ae zenon_H76 zenon_H290 zenon_H278 zenon_H245 zenon_H14b zenon_H15e zenon_Hc6 zenon_H71 zenon_H85 zenon_H1f zenon_Hca zenon_H31 zenon_Ha4 zenon_H287 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_Hf4 zenon_H13c zenon_He9 zenon_H127. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.36 apply (zenon_L33_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.36 exact (zenon_H30 zenon_H2d). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.13/10.36 apply (zenon_L89_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.13/10.36 apply (zenon_L330_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.13/10.36 apply (zenon_L327_); trivial. % 10.13/10.36 apply (zenon_L187_); trivial. % 10.13/10.36 apply (zenon_L77_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.36 exact (zenon_H30 zenon_H2d). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.36 apply (zenon_L248_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.36 apply (zenon_L331_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.36 apply (zenon_L297_); trivial. % 10.13/10.36 apply (zenon_L71_); trivial. % 10.13/10.36 apply (zenon_L77_); trivial. % 10.13/10.36 (* end of lemma zenon_L332_ *) % 10.13/10.36 assert (zenon_L333_ : (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 10.13/10.36 do 0 intro. intros zenon_H154 zenon_Hc3 zenon_H252. % 10.13/10.36 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e3) (e1)))). % 10.13/10.36 intro zenon_D_pnotp. % 10.13/10.36 apply zenon_H154. % 10.13/10.36 rewrite <- zenon_D_pnotp. % 10.13/10.36 exact zenon_Hc3. % 10.13/10.36 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2bf]. % 10.13/10.36 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 10.13/10.36 congruence. % 10.13/10.36 apply zenon_H1b4. apply refl_equal. % 10.13/10.36 apply zenon_H2bf. apply sym_equal. exact zenon_H252. % 10.13/10.36 (* end of lemma zenon_L333_ *) % 10.13/10.36 assert (zenon_L334_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e0)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.36 do 0 intro. intros zenon_He0 zenon_He9 zenon_Ha5 zenon_H8b zenon_H104 zenon_Hc4 zenon_H13b zenon_H13d zenon_H17e zenon_Hda zenon_H8c zenon_Hbb zenon_Hdf zenon_H252 zenon_H154 zenon_Hce zenon_Hcd zenon_Hd3 zenon_Hd5. % 10.13/10.36 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.36 apply (zenon_L139_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.36 apply (zenon_L333_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.36 apply (zenon_L48_); trivial. % 10.13/10.36 apply (zenon_L49_); trivial. % 10.13/10.36 (* end of lemma zenon_L334_ *) % 10.13/10.36 assert (zenon_L335_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.36 do 0 intro. intros zenon_Hb6 zenon_H94 zenon_H99 zenon_H2b9 zenon_H9c zenon_H6b zenon_Hb3 zenon_H85 zenon_Hca zenon_H1f zenon_Hc0 zenon_Hd5 zenon_Hd3 zenon_Hcd zenon_Hce zenon_H154 zenon_Hdf zenon_Hbb zenon_H8c zenon_Hda zenon_H17e zenon_H13d zenon_H13b zenon_H104 zenon_H8b zenon_He9 zenon_He0 zenon_H71 zenon_Hc6. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.36 apply (zenon_L33_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.36 apply (zenon_L35_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.13/10.36 apply (zenon_L41_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.13/10.36 exact (zenon_H8c zenon_H91). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.13/10.36 apply (zenon_L47_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.13/10.36 apply (zenon_L44_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.13/10.36 apply (zenon_L334_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.13/10.36 exact (zenon_H71 zenon_H74). % 10.13/10.36 apply (zenon_L46_); trivial. % 10.13/10.36 (* end of lemma zenon_L335_ *) % 10.13/10.36 assert (zenon_L336_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 10.13/10.36 do 0 intro. intros zenon_H12a zenon_H9a zenon_H115 zenon_H6b zenon_Hb3 zenon_Ha3 zenon_Hef zenon_Hc6 zenon_Hfc zenon_H104 zenon_H100 zenon_Hf6 zenon_He0 zenon_Hf4 zenon_H122 zenon_H124 zenon_Hfd zenon_H252. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.13/10.36 apply (zenon_L70_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.13/10.36 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.13/10.36 apply (zenon_L76_); trivial. % 10.13/10.36 apply (zenon_L199_); trivial. % 10.13/10.36 (* end of lemma zenon_L336_ *) % 10.13/10.36 assert (zenon_L337_ : (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.13/10.36 do 0 intro. intros zenon_He9 zenon_H124 zenon_H122 zenon_Hfd zenon_Hf4 zenon_He0 zenon_Hf6 zenon_H100 zenon_H104 zenon_Hfc zenon_Hc6 zenon_Ha3 zenon_Hb6 zenon_H1f zenon_H94 zenon_H115 zenon_H6b zenon_Hb3 zenon_H12a zenon_H2b9 zenon_H171 zenon_H173 zenon_H24e zenon_H177 zenon_Hba zenon_H85 zenon_H12d zenon_H99 zenon_Hef. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.36 apply (zenon_L33_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.36 apply (zenon_L58_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.13/10.36 apply (zenon_L203_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.13/10.36 apply (zenon_L197_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.13/10.36 apply (zenon_L45_); trivial. % 10.13/10.36 apply (zenon_L336_); trivial. % 10.13/10.36 apply (zenon_L78_); trivial. % 10.13/10.36 apply (zenon_L71_); trivial. % 10.13/10.36 (* end of lemma zenon_L337_ *) % 10.13/10.36 assert (zenon_L338_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e2)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.36 do 0 intro. intros zenon_H281 zenon_H12d zenon_H85 zenon_H177 zenon_H24e zenon_H173 zenon_H171 zenon_H2b9 zenon_Hb3 zenon_H115 zenon_Hef zenon_H99 zenon_Hdf zenon_Hbb zenon_Hfc zenon_H15e zenon_He9 zenon_H1f zenon_H14b zenon_H15b zenon_H154 zenon_H104 zenon_H157 zenon_H100 zenon_Hf6 zenon_H124 zenon_H122 zenon_He0 zenon_Hc6 zenon_Ha3 zenon_H12a zenon_Hcd zenon_Hda zenon_Hf4 zenon_H6b zenon_H94 zenon_Hb6 zenon_Hfd zenon_H13b. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.13/10.36 apply (zenon_L29_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.13/10.36 apply (zenon_L337_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.13/10.36 apply (zenon_L98_); trivial. % 10.13/10.36 apply (zenon_L255_); trivial. % 10.13/10.36 (* end of lemma zenon_L338_ *) % 10.13/10.36 assert (zenon_L339_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (e2))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.36 do 0 intro. intros zenon_H1a3 zenon_Hda zenon_H157 zenon_H154 zenon_H15b zenon_H14b zenon_Hbb zenon_Hdf zenon_H281 zenon_H85 zenon_H177 zenon_H24e zenon_H173 zenon_H171 zenon_H2b9 zenon_He9 zenon_H124 zenon_H122 zenon_Hf4 zenon_He0 zenon_Hf6 zenon_H100 zenon_H104 zenon_Hfc zenon_Hc6 zenon_Ha3 zenon_Hb6 zenon_H1f zenon_H94 zenon_H115 zenon_H6b zenon_Hb3 zenon_H12a zenon_H12d zenon_H99 zenon_Hef zenon_H15e zenon_Hfd zenon_H13b. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.13/10.36 apply (zenon_L29_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.13/10.36 apply (zenon_L204_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.13/10.36 apply (zenon_L338_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.13/10.36 apply (zenon_L29_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.13/10.36 apply (zenon_L337_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.13/10.36 apply (zenon_L104_); trivial. % 10.13/10.36 apply (zenon_L255_); trivial. % 10.13/10.36 (* end of lemma zenon_L339_ *) % 10.13/10.36 assert (zenon_L340_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e2) (e3)) = (e2))) -> False). % 10.13/10.36 do 0 intro. intros zenon_He0 zenon_H13d zenon_Hbb zenon_Hef zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H135 zenon_H130 zenon_H31 zenon_H145 zenon_H101 zenon_Hf4 zenon_Hce zenon_Hcd zenon_H122. % 10.13/10.36 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.13/10.36 apply (zenon_L87_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.13/10.36 apply (zenon_L193_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.13/10.36 apply (zenon_L48_); trivial. % 10.13/10.36 exact (zenon_H122 zenon_Hd4). % 10.13/10.36 (* end of lemma zenon_L340_ *) % 10.13/10.36 assert (zenon_L341_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 10.13/10.36 do 0 intro. intros zenon_Hef zenon_H17c zenon_H104. % 10.13/10.36 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.13/10.36 cut (((e3) = (e3)) = ((e1) = (e3))). % 10.13/10.36 intro zenon_D_pnotp. % 10.13/10.36 apply zenon_H104. % 10.13/10.36 rewrite <- zenon_D_pnotp. % 10.13/10.36 exact zenon_Hea. % 10.13/10.36 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.36 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 10.13/10.36 congruence. % 10.13/10.36 cut (((op (e1) (e3)) = (e1)) = ((e3) = (e1))). % 10.13/10.36 intro zenon_D_pnotp. % 10.13/10.36 apply zenon_H105. % 10.13/10.36 rewrite <- zenon_D_pnotp. % 10.13/10.36 exact zenon_Hef. % 10.13/10.36 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.36 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 10.13/10.36 congruence. % 10.13/10.36 exact (zenon_H17d zenon_H17c). % 10.13/10.36 apply zenon_H98. apply refl_equal. % 10.13/10.36 apply zenon_Heb. apply refl_equal. % 10.13/10.36 apply zenon_Heb. apply refl_equal. % 10.13/10.36 (* end of lemma zenon_L341_ *) % 10.13/10.36 assert (zenon_L342_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H17e zenon_H13d zenon_H13b zenon_Ha3 zenon_H150 zenon_Hda zenon_Hef zenon_H104. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.36 apply (zenon_L85_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.36 exact (zenon_Ha3 zenon_Ha2). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.36 apply (zenon_L308_); trivial. % 10.13/10.36 apply (zenon_L341_); trivial. % 10.13/10.36 (* end of lemma zenon_L342_ *) % 10.13/10.36 assert (zenon_L343_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H15e zenon_H31 zenon_H99 zenon_Hb3 zenon_H6b zenon_H115 zenon_H94 zenon_H1f zenon_Hb6 zenon_H104 zenon_Hef zenon_Hda zenon_Ha3 zenon_H13b zenon_H13d zenon_H17e zenon_He5 zenon_Hfd. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.36 apply (zenon_L295_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.36 apply (zenon_L72_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.36 apply (zenon_L342_); trivial. % 10.13/10.36 apply (zenon_L103_); trivial. % 10.13/10.36 (* end of lemma zenon_L343_ *) % 10.13/10.36 assert (zenon_L344_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H24e zenon_H104 zenon_H119 zenon_H115 zenon_Hef zenon_Hc3 zenon_Hf4 zenon_H128 zenon_H99. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.13/10.36 apply (zenon_L99_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.13/10.36 apply (zenon_L65_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.13/10.36 apply (zenon_L193_); trivial. % 10.13/10.36 apply (zenon_L111_); trivial. % 10.13/10.36 (* end of lemma zenon_L344_ *) % 10.13/10.36 assert (zenon_L345_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.36 do 0 intro. intros zenon_Hb6 zenon_H6b zenon_H163 zenon_Hf4 zenon_H31 zenon_H124 zenon_H99 zenon_H171 zenon_H15b zenon_H135 zenon_H13b zenon_Hfd zenon_H157 zenon_H158 zenon_H1b7 zenon_H94 zenon_H2ab zenon_Hca zenon_H1f zenon_Hc0 zenon_Hc3 zenon_H85 zenon_H71 zenon_Hc6. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.36 apply (zenon_L33_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.36 apply (zenon_L207_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.36 apply (zenon_L217_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.36 apply (zenon_L35_); trivial. % 10.13/10.36 apply (zenon_L226_); trivial. % 10.13/10.36 apply (zenon_L47_); trivial. % 10.13/10.36 (* end of lemma zenon_L345_ *) % 10.13/10.36 assert (zenon_L346_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.36 do 0 intro. intros zenon_Hb6 zenon_H94 zenon_Hf4 zenon_H124 zenon_H1b7 zenon_H99 zenon_H12a zenon_H24b zenon_He5 zenon_H115 zenon_H266 zenon_H100 zenon_H13b zenon_H135 zenon_H15b zenon_H163 zenon_H171 zenon_H31 zenon_H104 zenon_Hfd zenon_He9 zenon_Hba zenon_H2ab zenon_H6b zenon_H30 zenon_H12d zenon_Hca zenon_H1f zenon_Hc0 zenon_Hc3 zenon_H85 zenon_H71 zenon_Hc6. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.36 apply (zenon_L33_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.36 exact (zenon_H30 zenon_H2d). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.36 apply (zenon_L45_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.36 apply (zenon_L236_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.13/10.36 apply (zenon_L44_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.13/10.36 apply (zenon_L45_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.13/10.36 exact (zenon_H71 zenon_H74). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.36 apply (zenon_L121_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.36 apply (zenon_L107_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.36 exact (zenon_H163 zenon_H103). % 10.13/10.36 apply (zenon_L216_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.13/10.36 apply (zenon_L225_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.13/10.36 apply (zenon_L73_); trivial. % 10.13/10.36 apply (zenon_L77_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.36 apply (zenon_L35_); trivial. % 10.13/10.36 apply (zenon_L227_); trivial. % 10.13/10.36 apply (zenon_L47_); trivial. % 10.13/10.36 (* end of lemma zenon_L346_ *) % 10.13/10.36 assert (zenon_L347_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.13/10.36 do 0 intro. intros zenon_H281 zenon_Hc6 zenon_H71 zenon_H85 zenon_Hc3 zenon_Hc0 zenon_H1f zenon_Hca zenon_H12d zenon_H30 zenon_H6b zenon_H2ab zenon_He9 zenon_H104 zenon_H31 zenon_H171 zenon_H163 zenon_H15b zenon_H135 zenon_H100 zenon_H266 zenon_H115 zenon_He5 zenon_H24b zenon_H12a zenon_H99 zenon_H124 zenon_Hf4 zenon_H94 zenon_Hb6 zenon_H1b2 zenon_H1b7 zenon_Hfd zenon_H13b. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.13/10.36 apply (zenon_L57_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.13/10.36 apply (zenon_L346_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.13/10.36 apply (zenon_L153_); trivial. % 10.13/10.36 apply (zenon_L255_); trivial. % 10.13/10.36 (* end of lemma zenon_L347_ *) % 10.13/10.36 assert (zenon_L348_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.36 do 0 intro. intros zenon_Hb6 zenon_H94 zenon_H29d zenon_H189 zenon_H99 zenon_H12a zenon_Hf6 zenon_H104 zenon_Hfd zenon_He9 zenon_Hba zenon_Hf4 zenon_H2ab zenon_H6b zenon_H37 zenon_H12d zenon_Hca zenon_H1f zenon_Hc0 zenon_Hc3 zenon_H85 zenon_H71 zenon_Hc6. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.36 apply (zenon_L33_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.36 apply (zenon_L7_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.36 apply (zenon_L45_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.36 apply (zenon_L236_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.36 apply (zenon_L279_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.36 apply (zenon_L35_); trivial. % 10.13/10.36 apply (zenon_L280_); trivial. % 10.13/10.36 apply (zenon_L47_); trivial. % 10.13/10.36 (* end of lemma zenon_L348_ *) % 10.13/10.36 assert (zenon_L349_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> False). % 10.13/10.36 do 0 intro. intros zenon_Hb6 zenon_H1f zenon_H94 zenon_H6b zenon_H8b zenon_H99 zenon_Hdf zenon_Hbb zenon_Hb9 zenon_H8c zenon_Hcd zenon_Hda zenon_H85. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.36 apply (zenon_L33_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.36 apply (zenon_L35_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.13/10.36 apply (zenon_L43_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.13/10.36 exact (zenon_H8c zenon_H91). % 10.13/10.36 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.13/10.36 apply (zenon_L50_); trivial. % 10.13/10.36 apply (zenon_L51_); trivial. % 10.13/10.36 (* end of lemma zenon_L349_ *) % 10.13/10.36 assert (zenon_L350_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H145 zenon_H1f zenon_H31 zenon_H130 zenon_Hb9 zenon_H135 zenon_H67 zenon_H26e. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H131 | zenon_intro zenon_H146 ]. % 10.13/10.36 apply (zenon_L81_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H133 | zenon_intro zenon_H147 ]. % 10.13/10.36 apply (zenon_L82_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H136 | zenon_intro zenon_H13b ]. % 10.13/10.36 apply (zenon_L83_); trivial. % 10.13/10.36 apply (zenon_L221_); trivial. % 10.13/10.36 (* end of lemma zenon_L350_ *) % 10.13/10.36 assert (zenon_L351_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.36 do 0 intro. intros zenon_H244 zenon_H13d zenon_H13c zenon_H175 zenon_H104 zenon_H1f9 zenon_H145 zenon_H1f zenon_H31 zenon_H130 zenon_Hb9 zenon_H135 zenon_H26e. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.13/10.36 apply (zenon_L85_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.13/10.36 apply (zenon_L187_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.13/10.36 exact (zenon_H1f9 zenon_H1ed). % 10.13/10.36 apply (zenon_L350_); trivial. % 10.13/10.36 (* end of lemma zenon_L351_ *) % 10.13/10.36 assert (zenon_L352_ : (((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 (e0) (e0)) = (op (e0) (e1)))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e1) = (e3))) -> False). % 10.13/10.36 do 0 intro. intros zenon_Hb6 zenon_H12d zenon_H37 zenon_Hfd zenon_H13c zenon_H145 zenon_H135 zenon_H26e zenon_H85 zenon_H8c zenon_Hb3 zenon_H6b zenon_H9c zenon_H2b9 zenon_H18a zenon_H130 zenon_H99 zenon_H186 zenon_H244 zenon_H8b zenon_H142 zenon_H1f zenon_H31 zenon_H94 zenon_Hbb zenon_Hb9 zenon_H177 zenon_H13d zenon_H17e zenon_He9 zenon_H1f9 zenon_H104. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.36 apply (zenon_L33_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.36 apply (zenon_L35_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.36 apply (zenon_L7_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.36 exact (zenon_H6b zenon_H6f). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.13/10.36 apply (zenon_L41_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.13/10.36 exact (zenon_H8c zenon_H91). % 10.13/10.36 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.13/10.36 apply (zenon_L45_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.13/10.36 apply (zenon_L82_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.13/10.36 apply (zenon_L351_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.13/10.36 apply (zenon_L125_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.13/10.36 apply (zenon_L120_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.13/10.36 apply (zenon_L199_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.13/10.36 exact (zenon_H1f9 zenon_H1ed). % 10.13/10.36 apply (zenon_L286_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.13/10.36 apply (zenon_L82_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.13/10.36 apply (zenon_L111_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.13/10.36 apply (zenon_L125_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.13/10.36 apply (zenon_L120_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.13/10.36 apply (zenon_L77_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.13/10.36 exact (zenon_H1f9 zenon_H1ed). % 10.13/10.36 apply (zenon_L286_); trivial. % 10.13/10.36 (* end of lemma zenon_L352_ *) % 10.13/10.36 assert (zenon_L353_ : (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (e3)) = (e2)) -> False). % 10.13/10.36 do 0 intro. intros zenon_Hfd zenon_H67 zenon_Hd3. % 10.13/10.36 cut (((op (e3) (e3)) = (e3)) = ((e2) = (e3))). % 10.13/10.36 intro zenon_D_pnotp. % 10.13/10.36 apply zenon_Hfd. % 10.13/10.36 rewrite <- zenon_D_pnotp. % 10.13/10.36 exact zenon_H67. % 10.13/10.36 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.36 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 10.13/10.36 congruence. % 10.13/10.36 exact (zenon_H1ee zenon_Hd3). % 10.13/10.36 apply zenon_Heb. apply refl_equal. % 10.13/10.36 (* end of lemma zenon_L353_ *) % 10.13/10.36 assert (zenon_L354_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.13/10.36 do 0 intro. intros zenon_H244 zenon_H135 zenon_H152 zenon_H14b zenon_H119 zenon_H1f9 zenon_Hfd zenon_Hd3. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.13/10.36 apply (zenon_L211_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.13/10.36 apply (zenon_L90_); trivial. % 10.13/10.36 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.13/10.37 exact (zenon_H1f9 zenon_H1ed). % 10.13/10.37 apply (zenon_L353_); trivial. % 10.13/10.37 (* end of lemma zenon_L354_ *) % 10.13/10.37 assert (zenon_L355_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H47 zenon_H5a zenon_H150. % 10.13/10.37 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e0) (e2)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H47. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H5a. % 10.13/10.37 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 10.13/10.37 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 10.13/10.37 congruence. % 10.13/10.37 apply zenon_H97. apply refl_equal. % 10.13/10.37 apply zenon_H27e. apply sym_equal. exact zenon_H150. % 10.13/10.37 (* end of lemma zenon_L355_ *) % 10.13/10.37 assert (zenon_L356_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> False). % 10.13/10.37 do 0 intro. intros zenon_Hb6 zenon_H6b zenon_H8b zenon_H99 zenon_H17e zenon_H13d zenon_H13b zenon_H177 zenon_Hb9 zenon_Hbb zenon_H94 zenon_H31 zenon_H1f zenon_H142 zenon_H150 zenon_Hda zenon_He9. % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.37 apply (zenon_L33_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.37 exact (zenon_H6b zenon_H6f). % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.37 apply (zenon_L35_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.37 apply (zenon_L85_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.37 apply (zenon_L117_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.37 apply (zenon_L308_); trivial. % 10.13/10.37 apply (zenon_L119_); trivial. % 10.13/10.37 (* end of lemma zenon_L356_ *) % 10.13/10.37 assert (zenon_L357_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H18f zenon_Hfd zenon_H67. % 10.13/10.37 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H8b. zenon_intro zenon_H190. % 10.13/10.37 apply (zenon_and_s _ _ zenon_H190). zenon_intro zenon_H8c. zenon_intro zenon_H1c8. % 10.13/10.37 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.13/10.37 apply (zenon_L353_); trivial. % 10.13/10.37 (* end of lemma zenon_L357_ *) % 10.13/10.37 assert (zenon_L358_ : ((op (e0) (e0)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H31 zenon_H127 zenon_H1e5 zenon_Hcd zenon_H85 zenon_H2ab zenon_H289 zenon_H157 zenon_H154 zenon_H15b zenon_H171 zenon_H145 zenon_H135 zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H104 zenon_Hf4 zenon_H18d zenon_H1a3 zenon_He6 zenon_H186 zenon_H99 zenon_H18a zenon_Hdf zenon_Hda zenon_H17e zenon_He9 zenon_H15e zenon_Hfd zenon_H12d zenon_Hb6 zenon_H191 zenon_Hd5 zenon_H14b zenon_H182 zenon_H100 zenon_H124 zenon_H177 zenon_H1a2 zenon_H13d zenon_Hbb zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6b zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.37 apply (zenon_L54_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.37 apply (zenon_L90_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.37 apply (zenon_L91_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.13/10.37 apply (zenon_L54_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.37 apply (zenon_L33_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.37 exact (zenon_H6b zenon_H6f). % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.37 apply (zenon_L318_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.37 apply (zenon_L248_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.13/10.37 apply (zenon_L43_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.13/10.37 apply (zenon_L310_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.13/10.37 apply (zenon_L50_); trivial. % 10.13/10.37 apply (zenon_L51_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.37 apply (zenon_L296_); trivial. % 10.13/10.37 apply (zenon_L71_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.13/10.37 apply (zenon_L92_); trivial. % 10.13/10.37 apply (zenon_L184_); trivial. % 10.13/10.37 (* end of lemma zenon_L358_ *) % 10.13/10.37 assert (zenon_L359_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e1) (e0)) = (e3)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H94 zenon_H5a zenon_H13c. % 10.13/10.37 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H94. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H5a. % 10.13/10.37 cut (((e3) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H141]. % 10.13/10.37 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 10.13/10.37 congruence. % 10.13/10.37 apply zenon_H97. apply refl_equal. % 10.13/10.37 apply zenon_H141. apply sym_equal. exact zenon_H13c. % 10.13/10.37 (* end of lemma zenon_L359_ *) % 10.13/10.37 assert (zenon_L360_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H142 zenon_H1f zenon_H36 zenon_H177 zenon_Hbb zenon_Hb9 zenon_H94 zenon_H5a. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H95 | zenon_intro zenon_H143 ]. % 10.13/10.37 apply (zenon_L33_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H143); [ zenon_intro zenon_H6a | zenon_intro zenon_H144 ]. % 10.13/10.37 apply (zenon_L282_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H144); [ zenon_intro zenon_Hba | zenon_intro zenon_H13c ]. % 10.13/10.37 apply (zenon_L43_); trivial. % 10.13/10.37 apply (zenon_L359_); trivial. % 10.13/10.37 (* end of lemma zenon_L360_ *) % 10.13/10.37 assert (zenon_L361_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H15e zenon_H94 zenon_Hb9 zenon_Hbb zenon_H177 zenon_H36 zenon_H1f zenon_H142 zenon_H14b zenon_H127 zenon_H104 zenon_H16e zenon_He5 zenon_Hfd. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.37 apply (zenon_L360_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.37 apply (zenon_L90_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.37 apply (zenon_L105_); trivial. % 10.13/10.37 apply (zenon_L103_); trivial. % 10.13/10.37 (* end of lemma zenon_L361_ *) % 10.13/10.37 assert (zenon_L362_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H12d zenon_H30 zenon_H6b zenon_H13d zenon_Hb9 zenon_Hbb zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H135 zenon_H130 zenon_H31 zenon_H145 zenon_H99 zenon_H9a zenon_H2b9 zenon_H76 zenon_H290 zenon_H278 zenon_H287 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_H245 zenon_H150 zenon_H1e1 zenon_H18a zenon_H104 zenon_H186 zenon_H15e zenon_H177 zenon_H14b zenon_He5 zenon_H293 zenon_H171 zenon_H124 zenon_Hf4 zenon_H85 zenon_Hfd zenon_H13c zenon_H2ab zenon_He9 zenon_H127. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.37 exact (zenon_H30 zenon_H2d). % 10.13/10.37 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.37 exact (zenon_H6b zenon_H6f). % 10.13/10.37 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.37 apply (zenon_L248_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.13/10.37 apply (zenon_L59_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.13/10.37 apply (zenon_L107_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.13/10.37 apply (zenon_L102_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.13/10.37 apply (zenon_L361_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.13/10.37 apply (zenon_L297_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.13/10.37 apply (zenon_L102_); trivial. % 10.13/10.37 apply (zenon_L303_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.13/10.37 apply (zenon_L310_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.13/10.37 apply (zenon_L45_); trivial. % 10.13/10.37 apply (zenon_L199_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.37 apply (zenon_L35_); trivial. % 10.13/10.37 apply (zenon_L87_); trivial. % 10.13/10.37 apply (zenon_L77_); trivial. % 10.13/10.37 (* end of lemma zenon_L362_ *) % 10.13/10.37 assert (zenon_L363_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e2) (e0)) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H1de zenon_H1e1 zenon_Hb9 zenon_Hb6 zenon_H124 zenon_H171 zenon_H293 zenon_H14b zenon_H177 zenon_H15e zenon_H245 zenon_H28c zenon_H1b2 zenon_Hc0 zenon_H287 zenon_H278 zenon_H290 zenon_H76 zenon_H142 zenon_H138 zenon_Hbb zenon_H12d zenon_H30 zenon_H6b zenon_H99 zenon_H18a zenon_H130 zenon_H104 zenon_H186 zenon_H2b9 zenon_Hda zenon_H13d zenon_H17e zenon_H135 zenon_H31 zenon_H1f zenon_H145 zenon_Hf4 zenon_H85 zenon_H94 zenon_H2ab zenon_He9 zenon_H127 zenon_H47 zenon_H289 zenon_He5 zenon_Hfd. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.37 apply (zenon_L295_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.37 apply (zenon_L90_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.13/10.37 apply (zenon_L355_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.37 apply (zenon_L33_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.37 exact (zenon_H6b zenon_H6f). % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.37 apply (zenon_L362_); trivial. % 10.13/10.37 apply (zenon_L316_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.13/10.37 apply (zenon_L92_); trivial. % 10.13/10.37 apply (zenon_L171_); trivial. % 10.13/10.37 apply (zenon_L103_); trivial. % 10.13/10.37 (* end of lemma zenon_L363_ *) % 10.13/10.37 assert (zenon_L364_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H12d zenon_H37 zenon_H1f zenon_H6b zenon_H103 zenon_H150 zenon_He9 zenon_H127. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.37 apply (zenon_L7_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.37 exact (zenon_H6b zenon_H6f). % 10.13/10.37 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.37 apply (zenon_L102_); trivial. % 10.13/10.37 apply (zenon_L77_); trivial. % 10.13/10.37 (* end of lemma zenon_L364_ *) % 10.13/10.37 assert (zenon_L365_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H15e zenon_H31 zenon_H14b zenon_He9 zenon_H6b zenon_H1f zenon_H37 zenon_H12d zenon_H15b zenon_Hfd zenon_Hb9 zenon_H154 zenon_H127 zenon_H104 zenon_H103 zenon_H157. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.37 apply (zenon_L295_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.37 apply (zenon_L90_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.37 apply (zenon_L364_); trivial. % 10.13/10.37 apply (zenon_L95_); trivial. % 10.13/10.37 (* end of lemma zenon_L365_ *) % 10.13/10.37 assert (zenon_L366_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 10.13/10.37 do 0 intro. intros zenon_Hce zenon_H16e zenon_H103. % 10.13/10.37 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_Hce. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H16e. % 10.13/10.37 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H16b]. % 10.13/10.37 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 10.13/10.37 congruence. % 10.13/10.37 apply zenon_H49. apply refl_equal. % 10.13/10.37 apply zenon_H16b. apply sym_equal. exact zenon_H103. % 10.13/10.37 (* end of lemma zenon_L366_ *) % 10.13/10.37 assert (zenon_L367_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H15e zenon_H14b zenon_H127 zenon_He9 zenon_H103 zenon_H6b zenon_H1f zenon_H37 zenon_H12d zenon_H198 zenon_H104. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.37 apply (zenon_L54_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.37 apply (zenon_L90_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.37 apply (zenon_L364_); trivial. % 10.13/10.37 apply (zenon_L135_); trivial. % 10.13/10.37 (* end of lemma zenon_L367_ *) % 10.13/10.37 assert (zenon_L368_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H1e6 zenon_H1a2 zenon_H157 zenon_H154 zenon_Hb9 zenon_Hfd zenon_H15b zenon_Hce zenon_H15e zenon_H14b zenon_He9 zenon_H6b zenon_H1f zenon_H37 zenon_H12d zenon_H104. % 10.13/10.37 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H127. zenon_intro zenon_H1e7. % 10.13/10.37 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1e5. zenon_intro zenon_H80. % 10.13/10.37 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.13/10.37 apply (zenon_L365_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.37 apply (zenon_L54_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.37 apply (zenon_L99_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.37 apply (zenon_L364_); trivial. % 10.13/10.37 apply (zenon_L95_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.13/10.37 apply (zenon_L366_); trivial. % 10.13/10.37 apply (zenon_L367_); trivial. % 10.13/10.37 (* end of lemma zenon_L368_ *) % 10.13/10.37 assert (zenon_L369_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H1f3 zenon_Hf4 zenon_H36. % 10.13/10.37 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H1ed. zenon_intro zenon_H1f4. % 10.13/10.37 apply (zenon_and_s _ _ zenon_H1f4). zenon_intro zenon_H1ee. zenon_intro zenon_H8f. % 10.13/10.37 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.13/10.37 apply (zenon_L310_); trivial. % 10.13/10.37 (* end of lemma zenon_L369_ *) % 10.13/10.37 assert (zenon_L370_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H2ab zenon_H29c zenon_H130 zenon_H1b2 zenon_H281 zenon_Hc0 zenon_H15b zenon_H298 zenon_He6 zenon_H269 zenon_H293 zenon_H28f zenon_H290 zenon_H287 zenon_H289 zenon_H1cb zenon_H1de zenon_H1ef zenon_H28c zenon_H284 zenon_Hca zenon_H171 zenon_H135 zenon_H1f zenon_H37 zenon_H47 zenon_H5b zenon_H85 zenon_H18d zenon_He9 zenon_H138 zenon_H94 zenon_Hbb zenon_Hd5 zenon_H124 zenon_H272 zenon_Hdf zenon_Hc6 zenon_Hda zenon_Hfd zenon_H157 zenon_H1a3 zenon_H13d zenon_H104 zenon_H278 zenon_H18a zenon_Hb6 zenon_H186 zenon_H17e zenon_H27c zenon_H24b zenon_H15e zenon_H202 zenon_H29b zenon_Hf4 zenon_H1f3 zenon_H90 zenon_H99 zenon_Ha5. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.37 apply (zenon_L278_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.37 apply (zenon_L369_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.37 exact (zenon_H90 zenon_H8b). % 10.13/10.37 apply (zenon_L71_); trivial. % 10.13/10.37 (* end of lemma zenon_L370_ *) % 10.13/10.37 assert (zenon_L371_ : (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H6b zenon_H91 zenon_H119 zenon_H2ab zenon_H29c zenon_H130 zenon_H1b2 zenon_H281 zenon_Hc0 zenon_H15b zenon_H298 zenon_He6 zenon_H269 zenon_H293 zenon_H28f zenon_H290 zenon_H287 zenon_H289 zenon_H1cb zenon_H1de zenon_H1ef zenon_H28c zenon_H284 zenon_Hca zenon_H171 zenon_H135 zenon_H1f zenon_H37 zenon_H47 zenon_H5b zenon_H85 zenon_H18d zenon_He9 zenon_H138 zenon_H94 zenon_Hbb zenon_Hd5 zenon_H124 zenon_H272 zenon_Hdf zenon_Hc6 zenon_Hda zenon_Hfd zenon_H157 zenon_H1a3 zenon_H13d zenon_H104 zenon_H278 zenon_H18a zenon_Hb6 zenon_H186 zenon_H17e zenon_H27c zenon_H24b zenon_H15e zenon_H202 zenon_H29b zenon_Hf4 zenon_H1f3 zenon_H90 zenon_H99. % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.37 apply (zenon_L33_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.37 exact (zenon_H6b zenon_H6f). % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.37 apply (zenon_L69_); trivial. % 10.13/10.37 apply (zenon_L370_); trivial. % 10.13/10.37 (* end of lemma zenon_L371_ *) % 10.13/10.37 assert (zenon_L372_ : ((op (e3) (e1)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H128 zenon_H17a zenon_H91. % 10.13/10.37 apply (zenon_notand_s _ _ ax15); [ zenon_intro zenon_H11e | zenon_intro zenon_H2c0 ]. % 10.13/10.37 apply zenon_H11e. apply sym_equal. exact zenon_H91. % 10.13/10.37 apply (zenon_notand_s _ _ zenon_H2c0); [ zenon_intro zenon_H2c1 | zenon_intro zenon_H19a ]. % 10.13/10.37 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.37 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((e3) = (op (e1) (op (e1) (e1))))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2c1. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_Hae. % 10.13/10.37 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.37 cut (((op (e1) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 10.13/10.37 congruence. % 10.13/10.37 cut (((op (e1) (e2)) = (e3)) = ((op (e1) (op (e1) (e1))) = (e3))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2c2. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H17a. % 10.13/10.37 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.37 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 10.13/10.37 congruence. % 10.13/10.37 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.37 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e1) (e1))))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H11c. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_Hae. % 10.13/10.37 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.37 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 10.13/10.37 congruence. % 10.13/10.37 apply (zenon_L66_); trivial. % 10.13/10.37 apply zenon_Haf. apply refl_equal. % 10.13/10.37 apply zenon_Haf. apply refl_equal. % 10.13/10.37 apply zenon_Heb. apply refl_equal. % 10.13/10.37 apply zenon_Haf. apply refl_equal. % 10.13/10.37 apply zenon_Haf. apply refl_equal. % 10.13/10.37 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.13/10.37 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((e0) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H19a. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_Ha7. % 10.13/10.37 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.13/10.37 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H19d]. % 10.13/10.37 congruence. % 10.13/10.37 cut (((op (e3) (e1)) = (e0)) = ((op (op (e1) (op (e1) (e1))) (e1)) = (e0))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H19d. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H128. % 10.13/10.37 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.37 cut (((op (e3) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 10.13/10.37 congruence. % 10.13/10.37 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.13/10.37 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((op (e3) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2c3. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_Ha7. % 10.13/10.37 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.13/10.37 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2c4]. % 10.13/10.37 congruence. % 10.13/10.37 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.37 cut (((op (e1) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 10.13/10.37 congruence. % 10.13/10.37 cut (((op (e1) (e2)) = (e3)) = ((op (e1) (op (e1) (e1))) = (e3))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2c2. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H17a. % 10.13/10.37 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.13/10.37 cut (((op (e1) (e2)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 10.13/10.37 congruence. % 10.13/10.37 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.13/10.37 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e2)) = (op (e1) (op (e1) (e1))))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H11c. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_Hae. % 10.13/10.37 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.13/10.37 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H118]. % 10.13/10.37 congruence. % 10.13/10.37 apply (zenon_L66_); trivial. % 10.13/10.37 apply zenon_Haf. apply refl_equal. % 10.13/10.37 apply zenon_Haf. apply refl_equal. % 10.13/10.37 apply zenon_Heb. apply refl_equal. % 10.13/10.37 apply zenon_H98. apply refl_equal. % 10.13/10.37 apply zenon_Ha8. apply refl_equal. % 10.13/10.37 apply zenon_Ha8. apply refl_equal. % 10.13/10.37 apply zenon_H84. apply refl_equal. % 10.13/10.37 apply zenon_Ha8. apply refl_equal. % 10.13/10.37 apply zenon_Ha8. apply refl_equal. % 10.13/10.37 (* end of lemma zenon_L372_ *) % 10.13/10.37 assert (zenon_L373_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H17e zenon_H104 zenon_H6a zenon_Hfd zenon_H91 zenon_H128 zenon_H24b zenon_H158. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.37 apply (zenon_L248_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.37 apply (zenon_L237_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.37 apply (zenon_L372_); trivial. % 10.13/10.37 apply (zenon_L253_); trivial. % 10.13/10.37 (* end of lemma zenon_L373_ *) % 10.13/10.37 assert (zenon_L374_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H2ab zenon_H158 zenon_H24b zenon_H128 zenon_H91 zenon_Hfd zenon_H104 zenon_H17e zenon_Hf4 zenon_H1f3 zenon_H90 zenon_H99 zenon_Ha5. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.37 apply (zenon_L373_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.37 apply (zenon_L369_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.37 exact (zenon_H90 zenon_H8b). % 10.13/10.37 apply (zenon_L71_); trivial. % 10.13/10.37 (* end of lemma zenon_L374_ *) % 10.13/10.37 assert (zenon_L375_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e3)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H2c5 zenon_Hfd zenon_H158 zenon_Hf4 zenon_Hef zenon_Hc7 zenon_H85 zenon_H1ee. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.13/10.37 apply (zenon_L103_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.13/10.37 apply (zenon_L97_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.13/10.37 apply (zenon_L234_); trivial. % 10.13/10.37 exact (zenon_H1ee zenon_Hd3). % 10.13/10.37 (* end of lemma zenon_L375_ *) % 10.13/10.37 assert (zenon_L376_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H272 zenon_He9 zenon_H99 zenon_H90 zenon_H1f3 zenon_H17e zenon_H104 zenon_H91 zenon_H128 zenon_H24b zenon_H2ab zenon_H1ee zenon_H85 zenon_Hef zenon_Hf4 zenon_H158 zenon_Hfd zenon_H2c5 zenon_H76. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.13/10.37 apply (zenon_L324_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.13/10.37 apply (zenon_L374_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.13/10.37 apply (zenon_L375_); trivial. % 10.13/10.37 exact (zenon_H76 zenon_H79). % 10.13/10.37 (* end of lemma zenon_L376_ *) % 10.13/10.37 assert (zenon_L377_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H245 zenon_H1f zenon_H130 zenon_H2c5 zenon_Hfd zenon_H158 zenon_Hf4 zenon_Hef zenon_H85 zenon_H1ee zenon_H2ab zenon_H24b zenon_H91 zenon_H104 zenon_H17e zenon_H1f3 zenon_H90 zenon_H99 zenon_H272 zenon_H1ed zenon_He9 zenon_H76. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.13/10.37 apply (zenon_L81_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.13/10.37 apply (zenon_L376_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.13/10.37 apply (zenon_L185_); trivial. % 10.13/10.37 exact (zenon_H76 zenon_H79). % 10.13/10.37 (* end of lemma zenon_L377_ *) % 10.13/10.37 assert (zenon_L378_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H289 zenon_H31 zenon_H76 zenon_H1ed zenon_H272 zenon_H90 zenon_H1f3 zenon_H91 zenon_H24b zenon_H2ab zenon_H1ee zenon_H85 zenon_H158 zenon_H2c5 zenon_H245 zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H104 zenon_Hf4 zenon_H18d zenon_H1a3 zenon_He6 zenon_H186 zenon_H99 zenon_H18a zenon_Hdf zenon_Hda zenon_H17e zenon_He9 zenon_H15e zenon_Hfd zenon_H12d zenon_Hb6 zenon_H191 zenon_Hd5 zenon_H14b zenon_H182 zenon_H100 zenon_H124 zenon_H177 zenon_H1a2 zenon_H13d zenon_Hbb zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6b zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.13/10.37 apply (zenon_L295_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.37 apply (zenon_L248_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.37 apply (zenon_L310_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.37 exact (zenon_H90 zenon_H8b). % 10.13/10.37 apply (zenon_L377_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.13/10.37 apply (zenon_L92_); trivial. % 10.13/10.37 apply (zenon_L184_); trivial. % 10.13/10.37 (* end of lemma zenon_L378_ *) % 10.13/10.37 assert (zenon_L379_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H29b zenon_H27c zenon_H278 zenon_H157 zenon_Hc6 zenon_H135 zenon_H171 zenon_Hca zenon_H284 zenon_H28c zenon_H287 zenon_H290 zenon_H28f zenon_H293 zenon_H269 zenon_H298 zenon_H15b zenon_H281 zenon_H29c zenon_Hcd zenon_H289 zenon_H31 zenon_H76 zenon_H1ed zenon_H272 zenon_H90 zenon_H1f3 zenon_H91 zenon_H24b zenon_H2ab zenon_H1ee zenon_H85 zenon_H2c5 zenon_H245 zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H104 zenon_Hf4 zenon_H18d zenon_H1a3 zenon_He6 zenon_H186 zenon_H99 zenon_H18a zenon_Hdf zenon_Hda zenon_H17e zenon_He9 zenon_H15e zenon_Hfd zenon_H12d zenon_Hb6 zenon_H191 zenon_Hd5 zenon_H14b zenon_H182 zenon_H100 zenon_H124 zenon_H177 zenon_H1a2 zenon_H13d zenon_Hbb zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6b zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.37 apply (zenon_L54_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.37 apply (zenon_L371_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.37 apply (zenon_L91_); trivial. % 10.13/10.37 apply (zenon_L378_); trivial. % 10.13/10.37 (* end of lemma zenon_L379_ *) % 10.13/10.37 assert (zenon_L380_ : ((op (e3) (e3)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H189 zenon_H133 zenon_H26e. % 10.13/10.37 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.13/10.37 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H26e. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_Hd6. % 10.13/10.37 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.37 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 10.13/10.37 congruence. % 10.13/10.37 cut (((op (e3) (e3)) = (e1)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H26f. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H189. % 10.13/10.37 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 10.13/10.37 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.37 congruence. % 10.13/10.37 apply zenon_Hd7. apply refl_equal. % 10.13/10.37 apply zenon_H134. apply sym_equal. exact zenon_H133. % 10.13/10.37 apply zenon_Hd7. apply refl_equal. % 10.13/10.37 apply zenon_Hd7. apply refl_equal. % 10.13/10.37 (* end of lemma zenon_L380_ *) % 10.13/10.37 assert (zenon_L381_ : (~((op (e0) (op (e0) (e0))) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H2c8 zenon_H5a. % 10.13/10.37 cut (((op (e0) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 10.13/10.37 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.37 congruence. % 10.13/10.37 apply zenon_H84. apply refl_equal. % 10.13/10.37 exact (zenon_H58 zenon_H5a). % 10.13/10.37 (* end of lemma zenon_L381_ *) % 10.13/10.37 assert (zenon_L382_ : ((op (e2) (e0)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (op (op (e0) (op (e0) (e0))) (e0)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_Hfa zenon_He5 zenon_H5a zenon_H2c9. % 10.13/10.37 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.13/10.37 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((e1) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2c9. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H256. % 10.13/10.37 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.13/10.37 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2ca]. % 10.13/10.37 congruence. % 10.13/10.37 cut (((op (e2) (e0)) = (e1)) = ((op (op (e0) (op (e0) (e0))) (e0)) = (e1))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2ca. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_Hfa. % 10.13/10.37 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.37 cut (((op (e2) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b4]. % 10.13/10.37 congruence. % 10.13/10.37 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.13/10.37 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((op (e2) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2b4. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H256. % 10.13/10.37 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.13/10.37 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2b5]. % 10.13/10.37 congruence. % 10.13/10.37 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.37 cut (((op (e0) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2b6]. % 10.13/10.37 congruence. % 10.13/10.37 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (op (e0) (e0))) = (e2))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2b6. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_He5. % 10.13/10.37 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.37 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2cb]. % 10.13/10.37 congruence. % 10.13/10.37 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.13/10.37 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e0) (e0))))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2cb. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H25d. % 10.13/10.37 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.13/10.37 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 10.13/10.37 congruence. % 10.13/10.37 apply (zenon_L381_); trivial. % 10.13/10.37 apply zenon_H25e. apply refl_equal. % 10.13/10.37 apply zenon_H25e. apply refl_equal. % 10.13/10.37 apply zenon_H87. apply refl_equal. % 10.13/10.37 apply zenon_H84. apply refl_equal. % 10.13/10.37 apply zenon_H257. apply refl_equal. % 10.13/10.37 apply zenon_H257. apply refl_equal. % 10.13/10.37 apply zenon_H98. apply refl_equal. % 10.13/10.37 apply zenon_H257. apply refl_equal. % 10.13/10.37 apply zenon_H257. apply refl_equal. % 10.13/10.37 (* end of lemma zenon_L382_ *) % 10.13/10.37 assert (zenon_L383_ : ((op (e2) (e0)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> False). % 10.13/10.37 do 0 intro. intros zenon_Hfa zenon_He5 zenon_H5a. % 10.13/10.37 apply (zenon_notand_s _ _ ax11); [ zenon_intro zenon_H197 | zenon_intro zenon_H2cc ]. % 10.13/10.37 apply zenon_H197. apply sym_equal. exact zenon_H5a. % 10.13/10.37 apply (zenon_notand_s _ _ zenon_H2cc); [ zenon_intro zenon_H2b8 | zenon_intro zenon_H2c9 ]. % 10.13/10.37 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.13/10.37 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e2) = (op (e0) (op (e0) (e0))))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2b8. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H25d. % 10.13/10.37 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.13/10.37 cut (((op (e0) (op (e0) (e0))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H2b6]. % 10.13/10.37 congruence. % 10.13/10.37 cut (((op (e0) (e3)) = (e2)) = ((op (e0) (op (e0) (e0))) = (e2))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2b6. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_He5. % 10.13/10.37 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.37 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2cb]. % 10.13/10.37 congruence. % 10.13/10.37 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.13/10.37 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e0) (e0))))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2cb. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H25d. % 10.13/10.37 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.13/10.37 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 10.13/10.37 congruence. % 10.13/10.37 apply (zenon_L381_); trivial. % 10.13/10.37 apply zenon_H25e. apply refl_equal. % 10.13/10.37 apply zenon_H25e. apply refl_equal. % 10.13/10.37 apply zenon_H87. apply refl_equal. % 10.13/10.37 apply zenon_H25e. apply refl_equal. % 10.13/10.37 apply zenon_H25e. apply refl_equal. % 10.13/10.37 apply (zenon_L382_); trivial. % 10.13/10.37 (* end of lemma zenon_L383_ *) % 10.13/10.37 assert (zenon_L384_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> False). % 10.13/10.37 do 0 intro. intros zenon_Hc0 zenon_H5a zenon_H152. % 10.13/10.37 cut (((op (e0) (e0)) = (e3)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_Hc0. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H5a. % 10.13/10.37 cut (((e3) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 10.13/10.37 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 10.13/10.37 congruence. % 10.13/10.37 apply zenon_H97. apply refl_equal. % 10.13/10.37 apply zenon_H264. apply sym_equal. exact zenon_H152. % 10.13/10.37 (* end of lemma zenon_L384_ *) % 10.13/10.37 assert (zenon_L385_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H28c zenon_H1f zenon_He5 zenon_H136 zenon_H135 zenon_Hc0 zenon_H5a. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H28d ]. % 10.13/10.37 apply (zenon_L44_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_Hfa | zenon_intro zenon_H28e ]. % 10.13/10.37 apply (zenon_L383_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H152 ]. % 10.13/10.37 apply (zenon_L83_); trivial. % 10.13/10.37 apply (zenon_L384_); trivial. % 10.13/10.37 (* end of lemma zenon_L385_ *) % 10.13/10.37 assert (zenon_L386_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H145 zenon_H128 zenon_H1de zenon_H26e zenon_H189 zenon_Hc0 zenon_H135 zenon_He5 zenon_H1f zenon_H28c zenon_H5a zenon_H130. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H131 | zenon_intro zenon_H146 ]. % 10.13/10.37 apply (zenon_L220_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H133 | zenon_intro zenon_H147 ]. % 10.13/10.37 apply (zenon_L380_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H136 | zenon_intro zenon_H13b ]. % 10.13/10.37 apply (zenon_L385_); trivial. % 10.13/10.37 apply (zenon_L133_); trivial. % 10.13/10.37 (* end of lemma zenon_L386_ *) % 10.13/10.37 assert (zenon_L387_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H67 zenon_H1ed zenon_H2cd. % 10.13/10.37 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.13/10.37 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2cd. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_Hd6. % 10.13/10.37 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.37 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2ce]. % 10.13/10.37 congruence. % 10.13/10.37 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H2ce. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H67. % 10.13/10.37 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2a7]. % 10.13/10.37 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.37 congruence. % 10.13/10.37 apply zenon_Hd7. apply refl_equal. % 10.13/10.37 apply zenon_H2a7. apply sym_equal. exact zenon_H1ed. % 10.13/10.37 apply zenon_Hd7. apply refl_equal. % 10.13/10.37 apply zenon_Hd7. apply refl_equal. % 10.13/10.37 (* end of lemma zenon_L387_ *) % 10.13/10.37 assert (zenon_L388_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H1f3 zenon_H67 zenon_H2cd. % 10.13/10.37 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H1ed. zenon_intro zenon_H1f4. % 10.13/10.37 apply (zenon_L387_); trivial. % 10.13/10.37 (* end of lemma zenon_L388_ *) % 10.13/10.37 assert (zenon_L389_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H2cf zenon_H76 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_He5 zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H128 zenon_H145 zenon_H1ee zenon_H1f3 zenon_H2cd. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2cf); [ zenon_intro zenon_H79 | zenon_intro zenon_H2d0 ]. % 10.13/10.37 exact (zenon_H76 zenon_H79). % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2d0); [ zenon_intro zenon_H189 | zenon_intro zenon_H2d1 ]. % 10.13/10.37 apply (zenon_L386_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H67 ]. % 10.13/10.37 exact (zenon_H1ee zenon_Hd3). % 10.13/10.37 apply (zenon_L388_); trivial. % 10.13/10.37 (* end of lemma zenon_L389_ *) % 10.13/10.37 assert (zenon_L390_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H245 zenon_H2cd zenon_H1f3 zenon_H1ee zenon_H145 zenon_H1de zenon_H26e zenon_Hc0 zenon_H135 zenon_He5 zenon_H1f zenon_H28c zenon_H5a zenon_H130 zenon_H2cf zenon_H1ed zenon_He9 zenon_H76. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.13/10.37 apply (zenon_L81_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.13/10.37 apply (zenon_L389_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.13/10.37 apply (zenon_L185_); trivial. % 10.13/10.37 exact (zenon_H76 zenon_H79). % 10.13/10.37 (* end of lemma zenon_L390_ *) % 10.13/10.37 assert (zenon_L391_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H289 zenon_H76 zenon_He9 zenon_H1ed zenon_H2cf zenon_H28c zenon_He5 zenon_H135 zenon_H26e zenon_H145 zenon_H1ee zenon_H1f3 zenon_H2cd zenon_H245 zenon_H104 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6a zenon_H94 zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.13/10.37 apply (zenon_L390_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.13/10.37 apply (zenon_L248_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.13/10.37 apply (zenon_L92_); trivial. % 10.13/10.37 apply (zenon_L261_); trivial. % 10.13/10.37 (* end of lemma zenon_L391_ *) % 10.13/10.37 assert (zenon_L392_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e1)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> False). % 10.13/10.37 do 0 intro. intros zenon_Hb6 zenon_H6b zenon_H119 zenon_H2ab zenon_H1ef zenon_Hb9 zenon_Hc0 zenon_H1de zenon_H94 zenon_H1cb zenon_H130 zenon_H1b2 zenon_H138 zenon_H18d zenon_H1f zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_H104 zenon_H245 zenon_H2cd zenon_H1f3 zenon_H1ee zenon_H145 zenon_H26e zenon_H135 zenon_He5 zenon_H28c zenon_H2cf zenon_H1ed zenon_He9 zenon_H76 zenon_H289 zenon_H91 zenon_Hf4 zenon_H90 zenon_H99. % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.37 apply (zenon_L33_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.37 exact (zenon_H6b zenon_H6f). % 10.13/10.37 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.37 apply (zenon_L69_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.13/10.37 apply (zenon_L391_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.13/10.37 apply (zenon_L310_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.13/10.37 exact (zenon_H90 zenon_H8b). % 10.13/10.37 apply (zenon_L71_); trivial. % 10.13/10.37 (* end of lemma zenon_L392_ *) % 10.13/10.37 assert (zenon_L393_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H15e zenon_H99 zenon_H90 zenon_Hf4 zenon_H91 zenon_H289 zenon_H76 zenon_He9 zenon_H2cf zenon_H28c zenon_H135 zenon_H26e zenon_H145 zenon_H1ee zenon_H1f3 zenon_H2cd zenon_H245 zenon_H104 zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H94 zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef zenon_H2ab zenon_H6b zenon_Hb6 zenon_H27c zenon_H1ed zenon_He5 zenon_Hfd. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.13/10.37 apply (zenon_L390_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.13/10.37 apply (zenon_L392_); trivial. % 10.13/10.37 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.13/10.37 apply (zenon_L252_); trivial. % 10.13/10.37 apply (zenon_L103_); trivial. % 10.13/10.37 (* end of lemma zenon_L393_ *) % 10.13/10.37 assert (zenon_L394_ : (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e0)) -> False). % 10.13/10.37 do 0 intro. intros zenon_H99 zenon_H6a zenon_H95. % 10.13/10.37 cut (((op (e1) (e0)) = (e1)) = ((e0) = (e1))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H99. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_H6a. % 10.13/10.37 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.37 cut (((op (e1) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H2d2]. % 10.13/10.37 congruence. % 10.13/10.37 exact (zenon_H2d2 zenon_H95). % 10.13/10.37 apply zenon_H98. apply refl_equal. % 10.13/10.37 (* end of lemma zenon_L394_ *) % 10.13/10.37 assert (zenon_L395_ : ((op (e3) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.37 do 0 intro. intros zenon_H67 zenon_H17c zenon_H29d. % 10.13/10.37 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.13/10.37 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.37 apply zenon_H29d. % 10.13/10.37 rewrite <- zenon_D_pnotp. % 10.13/10.37 exact zenon_Hd6. % 10.13/10.37 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.37 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H29e]. % 10.13/10.37 congruence. % 10.13/10.37 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 10.13/10.37 intro zenon_D_pnotp. % 10.13/10.38 apply zenon_H29e. % 10.13/10.38 rewrite <- zenon_D_pnotp. % 10.13/10.38 exact zenon_H67. % 10.13/10.38 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H27f]. % 10.13/10.38 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.38 congruence. % 10.13/10.38 apply zenon_Hd7. apply refl_equal. % 10.13/10.38 apply zenon_H27f. apply sym_equal. exact zenon_H17c. % 10.13/10.38 apply zenon_Hd7. apply refl_equal. % 10.13/10.38 apply zenon_Hd7. apply refl_equal. % 10.13/10.38 (* end of lemma zenon_L395_ *) % 10.13/10.38 assert (zenon_L396_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e3)) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.38 do 0 intro. intros zenon_H2cf zenon_H76 zenon_H26e zenon_H133 zenon_H1ee zenon_H17c zenon_H29d. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2cf); [ zenon_intro zenon_H79 | zenon_intro zenon_H2d0 ]. % 10.13/10.38 exact (zenon_H76 zenon_H79). % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2d0); [ zenon_intro zenon_H189 | zenon_intro zenon_H2d1 ]. % 10.13/10.38 apply (zenon_L380_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H67 ]. % 10.13/10.38 exact (zenon_H1ee zenon_Hd3). % 10.13/10.38 apply (zenon_L395_); trivial. % 10.13/10.38 (* end of lemma zenon_L396_ *) % 10.13/10.38 assert (zenon_L397_ : ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.38 do 0 intro. intros zenon_H67 zenon_H159 zenon_Hd5. % 10.13/10.38 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.13/10.38 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 10.13/10.38 intro zenon_D_pnotp. % 10.13/10.38 apply zenon_Hd5. % 10.13/10.38 rewrite <- zenon_D_pnotp. % 10.13/10.38 exact zenon_Hd6. % 10.13/10.38 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.38 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 10.13/10.38 congruence. % 10.13/10.38 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 10.13/10.38 intro zenon_D_pnotp. % 10.13/10.38 apply zenon_Hd8. % 10.13/10.38 rewrite <- zenon_D_pnotp. % 10.13/10.38 exact zenon_H67. % 10.13/10.38 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H15a]. % 10.13/10.38 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.13/10.38 congruence. % 10.13/10.38 apply zenon_Hd7. apply refl_equal. % 10.13/10.38 apply zenon_H15a. apply sym_equal. exact zenon_H159. % 10.13/10.38 apply zenon_Hd7. apply refl_equal. % 10.13/10.38 apply zenon_Hd7. apply refl_equal. % 10.13/10.38 (* end of lemma zenon_L397_ *) % 10.13/10.38 assert (zenon_L398_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.13/10.38 do 0 intro. intros zenon_H2cf zenon_H76 zenon_H198 zenon_He6 zenon_H1ee zenon_H159 zenon_Hd5. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2cf); [ zenon_intro zenon_H79 | zenon_intro zenon_H2d0 ]. % 10.13/10.38 exact (zenon_H76 zenon_H79). % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2d0); [ zenon_intro zenon_H189 | zenon_intro zenon_H2d1 ]. % 10.13/10.38 apply (zenon_L140_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H67 ]. % 10.13/10.38 exact (zenon_H1ee zenon_Hd3). % 10.13/10.38 apply (zenon_L397_); trivial. % 10.13/10.38 (* end of lemma zenon_L398_ *) % 10.13/10.38 assert (zenon_L399_ : (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.13/10.38 do 0 intro. intros zenon_H2d3 zenon_H104 zenon_H29d zenon_H133 zenon_H26e zenon_Hd5 zenon_H1ee zenon_He6 zenon_H198 zenon_H76 zenon_H2cf zenon_H1ed zenon_H2cd. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H158 | zenon_intro zenon_H2d4 ]. % 10.13/10.38 apply (zenon_L135_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H17c | zenon_intro zenon_H2d5 ]. % 10.13/10.38 apply (zenon_L396_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H159 | zenon_intro zenon_H67 ]. % 10.13/10.38 apply (zenon_L398_); trivial. % 10.13/10.38 apply (zenon_L387_); trivial. % 10.13/10.38 (* end of lemma zenon_L399_ *) % 10.13/10.38 assert (zenon_L400_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> False). % 10.13/10.38 do 0 intro. intros zenon_H2d6 zenon_Hdd zenon_Hf6 zenon_H100 zenon_H252 zenon_H154 zenon_H171 zenon_Ha2. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H2d7 ]. % 10.13/10.38 apply (zenon_L137_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H101 | zenon_intro zenon_H2d8 ]. % 10.13/10.38 apply (zenon_L61_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2d8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H120 ]. % 10.13/10.38 apply (zenon_L333_); trivial. % 10.13/10.38 apply (zenon_L257_); trivial. % 10.13/10.38 (* end of lemma zenon_L400_ *) % 10.13/10.38 assert (zenon_L401_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 10.13/10.38 do 0 intro. intros zenon_H27c zenon_Hcd zenon_H2d9. % 10.13/10.38 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 10.13/10.38 intro zenon_D_pnotp. % 10.13/10.38 apply zenon_H27c. % 10.13/10.38 rewrite <- zenon_D_pnotp. % 10.13/10.38 exact zenon_Hcd. % 10.13/10.38 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2da]. % 10.13/10.38 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 10.13/10.38 congruence. % 10.13/10.38 apply zenon_H49. apply refl_equal. % 10.13/10.38 apply zenon_H2da. apply sym_equal. exact zenon_H2d9. % 10.13/10.38 (* end of lemma zenon_L401_ *) % 10.13/10.38 assert (zenon_L402_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.38 do 0 intro. intros zenon_H2db zenon_Hf4 zenon_H107 zenon_H2d6 zenon_Hf6 zenon_H100 zenon_H154 zenon_H171 zenon_Ha2 zenon_H289 zenon_H76 zenon_He9 zenon_H1ed zenon_H2cf zenon_H28c zenon_H135 zenon_H26e zenon_H145 zenon_H1f3 zenon_H2cd zenon_H245 zenon_H104 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6a zenon_H94 zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef zenon_H2c5 zenon_Hcd zenon_H27c zenon_H1ee. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H136 | zenon_intro zenon_H2dc ]. % 10.13/10.38 apply (zenon_L83_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H252 | zenon_intro zenon_H2dd ]. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.13/10.38 apply (zenon_L391_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.13/10.38 apply (zenon_L400_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.13/10.38 apply (zenon_L269_); trivial. % 10.13/10.38 exact (zenon_H1ee zenon_Hd3). % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H2d9 | zenon_intro zenon_Hd3 ]. % 10.13/10.38 apply (zenon_L401_); trivial. % 10.13/10.38 exact (zenon_H1ee zenon_Hd3). % 10.13/10.38 (* end of lemma zenon_L402_ *) % 10.13/10.38 assert (zenon_L403_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.38 do 0 intro. intros zenon_H298 zenon_He6 zenon_Hd5 zenon_H29d zenon_H2d3 zenon_Ha5 zenon_H99 zenon_H1ee zenon_H27c zenon_Hcd zenon_H2c5 zenon_H1ef zenon_Hb9 zenon_Hc0 zenon_H1de zenon_H94 zenon_H6a zenon_H1cb zenon_H130 zenon_H1b2 zenon_H138 zenon_H18d zenon_H1f zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_H104 zenon_H245 zenon_H2cd zenon_H1f3 zenon_H145 zenon_H135 zenon_H28c zenon_H2cf zenon_H1ed zenon_He9 zenon_H76 zenon_H289 zenon_Ha2 zenon_H171 zenon_H154 zenon_H100 zenon_Hf6 zenon_H2d6 zenon_Hf4 zenon_H2db zenon_H133 zenon_H26e. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.13/10.38 apply (zenon_L399_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.13/10.38 apply (zenon_L71_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.13/10.38 apply (zenon_L402_); trivial. % 10.13/10.38 apply (zenon_L380_); trivial. % 10.13/10.38 (* end of lemma zenon_L403_ *) % 10.13/10.38 assert (zenon_L404_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.38 do 0 intro. intros zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H189 zenon_H26e zenon_H1de zenon_H128 zenon_H145 zenon_Ha2 zenon_Hc4 zenon_H1cb zenon_Hb9 zenon_H1ee. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.13/10.38 apply (zenon_L386_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.13/10.38 apply (zenon_L137_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.13/10.38 apply (zenon_L162_); trivial. % 10.13/10.38 exact (zenon_H1ee zenon_Hd3). % 10.13/10.38 (* end of lemma zenon_L404_ *) % 10.13/10.38 assert (zenon_L405_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.38 do 0 intro. intros zenon_H18a zenon_H2db zenon_Hf4 zenon_H2d6 zenon_H100 zenon_H154 zenon_H171 zenon_H289 zenon_H76 zenon_He9 zenon_H1ed zenon_H2cf zenon_H1f3 zenon_H2cd zenon_H245 zenon_H104 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H18d zenon_H138 zenon_H1b2 zenon_H6a zenon_H94 zenon_H1ef zenon_Hcd zenon_H27c zenon_H99 zenon_Ha5 zenon_H2d3 zenon_H29d zenon_Hd5 zenon_He6 zenon_H298 zenon_Hf6 zenon_H14b zenon_H103 zenon_H278 zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H128 zenon_H145 zenon_Ha2 zenon_Hc4 zenon_H1cb zenon_Hb9 zenon_H1ee. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.13/10.38 apply (zenon_L403_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.13/10.38 apply (zenon_L124_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.13/10.38 apply (zenon_L245_); trivial. % 10.13/10.38 apply (zenon_L404_); trivial. % 10.13/10.38 (* end of lemma zenon_L405_ *) % 10.13/10.38 assert (zenon_L406_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.38 do 0 intro. intros zenon_H2db zenon_Hb9 zenon_H85 zenon_Hc7 zenon_H2d6 zenon_Hf6 zenon_H100 zenon_H154 zenon_H171 zenon_Ha2 zenon_H145 zenon_H128 zenon_H1de zenon_H26e zenon_H189 zenon_Hc0 zenon_H135 zenon_H1f zenon_H28c zenon_H5a zenon_H130 zenon_H2c5 zenon_Hcd zenon_H27c zenon_H1ee. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H136 | zenon_intro zenon_H2dc ]. % 10.13/10.38 apply (zenon_L83_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H252 | zenon_intro zenon_H2dd ]. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.13/10.38 apply (zenon_L386_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.13/10.38 apply (zenon_L400_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.13/10.38 apply (zenon_L234_); trivial. % 10.13/10.38 exact (zenon_H1ee zenon_Hd3). % 10.13/10.38 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H2d9 | zenon_intro zenon_Hd3 ]. % 10.13/10.38 apply (zenon_L401_); trivial. % 10.13/10.38 exact (zenon_H1ee zenon_Hd3). % 10.13/10.38 (* end of lemma zenon_L406_ *) % 10.13/10.38 assert (zenon_L407_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.38 do 0 intro. intros zenon_H18a zenon_Hf4 zenon_H289 zenon_H76 zenon_He9 zenon_H1ed zenon_H2cf zenon_H1f3 zenon_H2cd zenon_H245 zenon_H104 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H18d zenon_H138 zenon_H1b2 zenon_H1cb zenon_H6a zenon_H94 zenon_H1ef zenon_H2d3 zenon_H29d zenon_Hd5 zenon_He6 zenon_H298 zenon_H99 zenon_H103 zenon_H278 zenon_H2db zenon_Hb9 zenon_H85 zenon_Hc7 zenon_H2d6 zenon_Hf6 zenon_H100 zenon_H154 zenon_H171 zenon_Ha2 zenon_H145 zenon_H128 zenon_H1de zenon_H26e zenon_Hc0 zenon_H135 zenon_H1f zenon_H28c zenon_H5a zenon_H130 zenon_H2c5 zenon_Hcd zenon_H27c zenon_H1ee. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.13/10.38 apply (zenon_L399_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.13/10.38 apply (zenon_L84_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.13/10.38 apply (zenon_L402_); trivial. % 10.13/10.38 apply (zenon_L380_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.13/10.38 apply (zenon_L111_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.13/10.38 apply (zenon_L245_); trivial. % 10.13/10.38 apply (zenon_L406_); trivial. % 10.13/10.38 (* end of lemma zenon_L407_ *) % 10.13/10.38 assert (zenon_L408_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.38 do 0 intro. intros zenon_H272 zenon_Hc4 zenon_H14b zenon_H1ee zenon_H27c zenon_Hcd zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H128 zenon_H145 zenon_Ha2 zenon_H171 zenon_H154 zenon_H100 zenon_Hf6 zenon_H2d6 zenon_H85 zenon_Hb9 zenon_H2db zenon_H278 zenon_H103 zenon_H99 zenon_H298 zenon_He6 zenon_Hd5 zenon_H29d zenon_H2d3 zenon_H1ef zenon_H94 zenon_H6a zenon_H1cb zenon_H1b2 zenon_H138 zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_H104 zenon_H245 zenon_H2cd zenon_H1f3 zenon_H2cf zenon_H1ed zenon_He9 zenon_H289 zenon_Hf4 zenon_H18a zenon_H76. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.13/10.38 apply (zenon_L16_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.13/10.38 apply (zenon_L405_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.13/10.38 apply (zenon_L407_); trivial. % 10.13/10.38 exact (zenon_H76 zenon_H79). % 10.13/10.38 (* end of lemma zenon_L408_ *) % 10.13/10.38 assert (zenon_L409_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 10.13/10.38 do 0 intro. intros zenon_H17e zenon_H104 zenon_H6a zenon_Hdd zenon_Hc4 zenon_H186 zenon_H1ed zenon_H24b zenon_H158. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.38 apply (zenon_L248_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.38 apply (zenon_L137_); trivial. % 10.13/10.38 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.39 apply (zenon_L249_); trivial. % 10.13/10.39 apply (zenon_L253_); trivial. % 10.13/10.39 (* end of lemma zenon_L409_ *) % 10.13/10.39 assert (zenon_L410_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.39 do 0 intro. intros zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H189 zenon_H26e zenon_H1de zenon_H128 zenon_H145 zenon_H158 zenon_H24b zenon_H1ed zenon_H186 zenon_Hc4 zenon_H6a zenon_H104 zenon_H17e zenon_H1cb zenon_Hb9 zenon_H1ee. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.13/10.39 apply (zenon_L386_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.13/10.39 apply (zenon_L409_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.13/10.39 apply (zenon_L162_); trivial. % 10.13/10.39 exact (zenon_H1ee zenon_Hd3). % 10.13/10.39 (* end of lemma zenon_L410_ *) % 10.13/10.39 assert (zenon_L411_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.39 do 0 intro. intros zenon_H298 zenon_Ha5 zenon_H99 zenon_Hfc zenon_H9a zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H128 zenon_H145 zenon_H158 zenon_H24b zenon_H1ed zenon_H186 zenon_Hc4 zenon_H6a zenon_H104 zenon_H17e zenon_H1cb zenon_Hb9 zenon_H1ee. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.13/10.39 apply (zenon_L135_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.13/10.39 apply (zenon_L71_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.13/10.39 apply (zenon_L64_); trivial. % 10.13/10.39 apply (zenon_L410_); trivial. % 10.13/10.39 (* end of lemma zenon_L411_ *) % 10.13/10.39 assert (zenon_L412_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 10.13/10.39 do 0 intro. intros zenon_H28f zenon_H74 zenon_Hc7. % 10.13/10.39 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 10.13/10.39 intro zenon_D_pnotp. % 10.13/10.39 apply zenon_H28f. % 10.13/10.39 rewrite <- zenon_D_pnotp. % 10.13/10.39 exact zenon_H74. % 10.13/10.39 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 10.13/10.39 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.13/10.39 congruence. % 10.13/10.39 apply zenon_Hd0. apply refl_equal. % 10.13/10.39 apply zenon_Hc8. apply sym_equal. exact zenon_Hc7. % 10.13/10.39 (* end of lemma zenon_L412_ *) % 10.13/10.39 assert (zenon_L413_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.13/10.39 do 0 intro. intros zenon_H298 zenon_H2cd zenon_H1ed zenon_H2cf zenon_H76 zenon_He6 zenon_H1ee zenon_Hd5 zenon_H29d zenon_H104 zenon_H2d3 zenon_H138 zenon_H6a zenon_H9a zenon_H287 zenon_Hb9 zenon_Hce zenon_H16e zenon_H28f zenon_Hc7 zenon_H290 zenon_H133 zenon_H26e. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.13/10.39 apply (zenon_L399_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.13/10.39 apply (zenon_L84_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H74 | zenon_intro zenon_H291 ]. % 10.13/10.39 apply (zenon_L412_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H103 | zenon_intro zenon_H292 ]. % 10.13/10.39 apply (zenon_L366_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfc ]. % 10.13/10.39 apply (zenon_L299_); trivial. % 10.13/10.39 apply (zenon_L64_); trivial. % 10.13/10.39 apply (zenon_L380_); trivial. % 10.13/10.39 (* end of lemma zenon_L413_ *) % 10.13/10.39 assert (zenon_L414_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.13/10.39 do 0 intro. intros zenon_H145 zenon_H128 zenon_H1de zenon_H26e zenon_H290 zenon_Hc7 zenon_H28f zenon_H16e zenon_Hce zenon_H287 zenon_H9a zenon_H6a zenon_H138 zenon_H2d3 zenon_H104 zenon_H29d zenon_Hd5 zenon_H1ee zenon_He6 zenon_H76 zenon_H2cf zenon_H1ed zenon_H2cd zenon_H298 zenon_Hb9 zenon_H135 zenon_H5a zenon_H130. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H131 | zenon_intro zenon_H146 ]. % 10.13/10.39 apply (zenon_L220_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H133 | zenon_intro zenon_H147 ]. % 10.13/10.39 apply (zenon_L413_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H136 | zenon_intro zenon_H13b ]. % 10.13/10.39 apply (zenon_L83_); trivial. % 10.13/10.39 apply (zenon_L133_); trivial. % 10.13/10.39 (* end of lemma zenon_L414_ *) % 10.13/10.39 assert (zenon_L415_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.13/10.39 do 0 intro. intros zenon_H2ae zenon_H47 zenon_H1f zenon_H130 zenon_H5a zenon_H135 zenon_Hb9 zenon_H298 zenon_H2cd zenon_H2cf zenon_H76 zenon_He6 zenon_H1ee zenon_Hd5 zenon_H29d zenon_H104 zenon_H2d3 zenon_H138 zenon_H6a zenon_H287 zenon_Hce zenon_H16e zenon_H290 zenon_H26e zenon_H1de zenon_H128 zenon_H145 zenon_Hc7 zenon_H28f zenon_He9 zenon_H1ed. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.13/10.39 apply (zenon_L11_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.13/10.39 apply (zenon_L414_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.13/10.39 apply (zenon_L412_); trivial. % 10.13/10.39 apply (zenon_L185_); trivial. % 10.13/10.39 (* end of lemma zenon_L415_ *) % 10.13/10.39 assert (zenon_L416_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.39 do 0 intro. intros zenon_H272 zenon_H1cb zenon_H17e zenon_Hc4 zenon_H186 zenon_H24b zenon_H158 zenon_Hc0 zenon_H28c zenon_H2c5 zenon_H9a zenon_Hfc zenon_H99 zenon_H1ed zenon_He9 zenon_H28f zenon_H145 zenon_H128 zenon_H1de zenon_H26e zenon_H290 zenon_H16e zenon_Hce zenon_H287 zenon_H6a zenon_H138 zenon_H2d3 zenon_H104 zenon_H29d zenon_Hd5 zenon_H1ee zenon_He6 zenon_H2cf zenon_H2cd zenon_H298 zenon_Hb9 zenon_H135 zenon_H5a zenon_H130 zenon_H1f zenon_H47 zenon_H2ae zenon_H76. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.13/10.39 apply (zenon_L324_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.13/10.39 apply (zenon_L411_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.13/10.39 apply (zenon_L415_); trivial. % 10.13/10.39 exact (zenon_H76 zenon_H79). % 10.13/10.39 (* end of lemma zenon_L416_ *) % 10.13/10.39 assert (zenon_L417_ : (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> False). % 10.13/10.39 do 0 intro. intros zenon_H85 zenon_Hb9 zenon_Hc1. % 10.13/10.39 cut (((op (e2) (e0)) = (e2)) = ((e0) = (e2))). % 10.13/10.39 intro zenon_D_pnotp. % 10.13/10.39 apply zenon_H85. % 10.13/10.39 rewrite <- zenon_D_pnotp. % 10.13/10.39 exact zenon_Hb9. % 10.13/10.39 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.13/10.39 cut (((op (e2) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H2de]. % 10.13/10.39 congruence. % 10.13/10.39 exact (zenon_H2de zenon_Hc1). % 10.13/10.39 apply zenon_H87. apply refl_equal. % 10.13/10.39 (* end of lemma zenon_L417_ *) % 10.13/10.39 assert (zenon_L418_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 10.13/10.39 do 0 intro. intros zenon_H15b zenon_Hfd zenon_Hb9 zenon_Ha2 zenon_H171 zenon_He9 zenon_H74 zenon_H157 zenon_H158. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.13/10.39 apply (zenon_L92_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.13/10.39 apply (zenon_L257_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.13/10.39 apply (zenon_L319_); trivial. % 10.13/10.39 apply (zenon_L94_); trivial. % 10.13/10.39 (* end of lemma zenon_L418_ *) % 10.13/10.39 assert (zenon_L419_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 10.13/10.39 do 0 intro. intros zenon_H15b zenon_Ha2 zenon_H171 zenon_H1ee zenon_Hb9 zenon_H1cb zenon_H17e zenon_H104 zenon_H6a zenon_Hc4 zenon_H186 zenon_H1ed zenon_H24b zenon_H145 zenon_H128 zenon_H1de zenon_H26e zenon_Hc0 zenon_H135 zenon_H1f zenon_H28c zenon_H5a zenon_H130 zenon_H2c5 zenon_H9a zenon_H99 zenon_Ha5 zenon_H298 zenon_H157 zenon_H158. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.13/10.39 apply (zenon_L384_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.13/10.39 apply (zenon_L257_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.13/10.39 apply (zenon_L411_); trivial. % 10.13/10.39 apply (zenon_L94_); trivial. % 10.13/10.39 (* end of lemma zenon_L419_ *) % 10.13/10.39 assert (zenon_L420_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.13/10.39 do 0 intro. intros zenon_H94 zenon_H15b zenon_Hfd zenon_Hb9 zenon_H171 zenon_H157 zenon_H158 zenon_H245 zenon_H298 zenon_H99 zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H145 zenon_H24b zenon_Hc4 zenon_H6a zenon_H104 zenon_H17e zenon_H1cb zenon_H1ee zenon_H76 zenon_H47 zenon_H2ae zenon_H186 zenon_H1ed zenon_Ha5 zenon_He9. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.39 apply (zenon_L359_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.13/10.39 apply (zenon_L11_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.13/10.39 apply (zenon_L81_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.13/10.39 apply (zenon_L419_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.13/10.39 apply (zenon_L185_); trivial. % 10.13/10.39 exact (zenon_H76 zenon_H79). % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.13/10.39 apply (zenon_L418_); trivial. % 10.13/10.39 apply (zenon_L185_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.39 apply (zenon_L249_); trivial. % 10.13/10.39 apply (zenon_L119_); trivial. % 10.13/10.39 (* end of lemma zenon_L420_ *) % 10.13/10.39 assert (zenon_L421_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.13/10.39 do 0 intro. intros zenon_H42 zenon_H16e zenon_H99. % 10.13/10.39 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H98 ]. % 10.13/10.39 cut (((e1) = (e1)) = ((e0) = (e1))). % 10.13/10.39 intro zenon_D_pnotp. % 10.13/10.39 apply zenon_H99. % 10.13/10.39 rewrite <- zenon_D_pnotp. % 10.13/10.39 exact zenon_Hf7. % 10.13/10.39 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.13/10.39 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 10.13/10.39 congruence. % 10.13/10.39 cut (((op (e0) (e2)) = (e0)) = ((e1) = (e0))). % 10.13/10.39 intro zenon_D_pnotp. % 10.13/10.39 apply zenon_Hf8. % 10.13/10.39 rewrite <- zenon_D_pnotp. % 10.13/10.39 exact zenon_H42. % 10.13/10.39 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.13/10.39 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2df]. % 10.13/10.39 congruence. % 10.13/10.39 exact (zenon_H2df zenon_H16e). % 10.13/10.39 apply zenon_H84. apply refl_equal. % 10.13/10.39 apply zenon_H98. apply refl_equal. % 10.13/10.39 apply zenon_H98. apply refl_equal. % 10.13/10.39 (* end of lemma zenon_L421_ *) % 10.13/10.39 assert (zenon_L422_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.13/10.39 do 0 intro. intros zenon_H289 zenon_H158 zenon_H24b zenon_H91 zenon_Hca zenon_H17e zenon_H186 zenon_H28c zenon_H2c5 zenon_H99 zenon_H157 zenon_H171 zenon_H15b zenon_H2ae zenon_H135 zenon_H298 zenon_H2cd zenon_H2cf zenon_H76 zenon_He6 zenon_H1ee zenon_Hd5 zenon_H29d zenon_H2d3 zenon_H287 zenon_Hce zenon_H16e zenon_H290 zenon_H26e zenon_H145 zenon_H28f zenon_He9 zenon_H1ed zenon_H245 zenon_H85 zenon_H12d zenon_H272 zenon_Hb6 zenon_H104 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6a zenon_H94 zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.13/10.39 apply (zenon_L394_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.13/10.39 apply (zenon_L247_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.39 apply (zenon_L7_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.39 apply (zenon_L247_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.39 apply (zenon_L359_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.13/10.39 apply (zenon_L384_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.13/10.39 apply (zenon_L257_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.13/10.39 apply (zenon_L81_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.13/10.39 apply (zenon_L416_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.13/10.39 apply (zenon_L185_); trivial. % 10.13/10.39 exact (zenon_H76 zenon_H79). % 10.13/10.39 apply (zenon_L94_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.39 apply (zenon_L249_); trivial. % 10.13/10.39 apply (zenon_L253_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.39 apply (zenon_L248_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.13/10.39 apply (zenon_L417_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.13/10.39 apply (zenon_L92_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.13/10.39 apply (zenon_L257_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.13/10.39 apply (zenon_L416_); trivial. % 10.13/10.39 apply (zenon_L94_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.13/10.39 apply (zenon_L418_); trivial. % 10.13/10.39 apply (zenon_L414_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.39 apply (zenon_L372_); trivial. % 10.13/10.39 apply (zenon_L253_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.13/10.39 apply (zenon_L7_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.13/10.39 apply (zenon_L247_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.13/10.39 apply (zenon_L420_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.13/10.39 apply (zenon_L248_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.13/10.39 apply (zenon_L44_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.13/10.39 apply (zenon_L421_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.13/10.39 apply (zenon_L419_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.13/10.39 apply (zenon_L418_); trivial. % 10.13/10.39 apply (zenon_L185_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.13/10.39 apply (zenon_L418_); trivial. % 10.13/10.39 apply (zenon_L415_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.13/10.39 apply (zenon_L372_); trivial. % 10.13/10.39 apply (zenon_L253_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.13/10.39 apply (zenon_L248_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.13/10.39 apply (zenon_L92_); trivial. % 10.13/10.39 apply (zenon_L261_); trivial. % 10.13/10.39 (* end of lemma zenon_L422_ *) % 10.13/10.39 assert (zenon_L423_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.39 do 0 intro. intros zenon_H1f3 zenon_H128 zenon_H5a zenon_H1ef zenon_Hb9 zenon_Hc0 zenon_H1de zenon_H94 zenon_H6a zenon_H1cb zenon_H130 zenon_H1b2 zenon_H138 zenon_H18d zenon_H1f zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_H104 zenon_Hb6 zenon_H272 zenon_H12d zenon_H85 zenon_H245 zenon_H1ed zenon_He9 zenon_H28f zenon_H145 zenon_H26e zenon_H290 zenon_H16e zenon_Hce zenon_H287 zenon_H2d3 zenon_H29d zenon_Hd5 zenon_He6 zenon_H76 zenon_H2cf zenon_H2cd zenon_H298 zenon_H135 zenon_H2ae zenon_H15b zenon_H171 zenon_H157 zenon_H99 zenon_H2c5 zenon_H28c zenon_H186 zenon_H17e zenon_Hca zenon_H91 zenon_H24b zenon_H289 zenon_H269 zenon_H107 zenon_Hf4 zenon_H1ee. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.13/10.39 apply (zenon_L389_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H56 | zenon_intro zenon_H26a ]. % 10.13/10.39 apply (zenon_L16_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H198 | zenon_intro zenon_H26b ]. % 10.13/10.39 apply (zenon_L210_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_He5 | zenon_intro zenon_H158 ]. % 10.13/10.39 apply (zenon_L213_); trivial. % 10.13/10.39 apply (zenon_L422_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.13/10.39 apply (zenon_L269_); trivial. % 10.13/10.39 exact (zenon_H1ee zenon_Hd3). % 10.13/10.39 (* end of lemma zenon_L423_ *) % 10.13/10.39 assert (zenon_L424_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.13/10.39 do 0 intro. intros zenon_H245 zenon_H1f zenon_H130 zenon_H99 zenon_H175 zenon_H1ed zenon_He9 zenon_H76. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.13/10.39 apply (zenon_L81_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.13/10.39 apply (zenon_L111_); trivial. % 10.13/10.39 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.13/10.39 apply (zenon_L185_); trivial. % 10.13/10.39 exact (zenon_H76 zenon_H79). % 10.13/10.39 (* end of lemma zenon_L424_ *) % 10.13/10.39 assert (zenon_L425_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.13/10.39 do 0 intro. intros zenon_H18a zenon_H1f3 zenon_H1ef zenon_H94 zenon_H6a zenon_H1b2 zenon_H138 zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_H104 zenon_Hb6 zenon_H272 zenon_H12d zenon_H85 zenon_H28f zenon_H290 zenon_Hce zenon_H287 zenon_H2d3 zenon_H29d zenon_Hd5 zenon_He6 zenon_H2cf zenon_H2cd zenon_H298 zenon_H2ae zenon_H15b zenon_H171 zenon_H157 zenon_H186 zenon_H17e zenon_Hca zenon_H91 zenon_H24b zenon_H289 zenon_H269 zenon_Hf4 zenon_H76 zenon_He9 zenon_H1ed zenon_H99 zenon_H245 zenon_H16e zenon_H27c zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H128 zenon_H145 zenon_Ha2 zenon_Hc4 zenon_H1cb zenon_Hb9 zenon_H1ee. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.25/10.39 apply (zenon_L399_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.25/10.39 apply (zenon_L84_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.25/10.39 apply (zenon_L423_); trivial. % 10.25/10.39 apply (zenon_L404_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.25/10.39 apply (zenon_L424_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.25/10.39 apply (zenon_L320_); trivial. % 10.25/10.39 apply (zenon_L404_); trivial. % 10.25/10.39 (* end of lemma zenon_L425_ *) % 10.25/10.39 assert (zenon_L426_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> False). % 10.25/10.39 do 0 intro. intros zenon_H269 zenon_Ha5 zenon_H189 zenon_He6 zenon_Hdd zenon_H24b zenon_H157 zenon_H159. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H56 | zenon_intro zenon_H26a ]. % 10.25/10.39 apply (zenon_L270_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H198 | zenon_intro zenon_H26b ]. % 10.25/10.39 apply (zenon_L140_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_He5 | zenon_intro zenon_H158 ]. % 10.25/10.39 apply (zenon_L213_); trivial. % 10.25/10.39 apply (zenon_L94_); trivial. % 10.25/10.39 (* end of lemma zenon_L426_ *) % 10.25/10.39 assert (zenon_L427_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.25/10.39 do 0 intro. intros zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H128 zenon_H145 zenon_H159 zenon_H157 zenon_H24b zenon_He6 zenon_H189 zenon_Ha5 zenon_H269 zenon_H1cb zenon_Hb9 zenon_H1ee. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.25/10.39 apply (zenon_L386_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.25/10.39 apply (zenon_L426_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.25/10.39 apply (zenon_L162_); trivial. % 10.25/10.39 exact (zenon_H1ee zenon_Hd3). % 10.25/10.39 (* end of lemma zenon_L427_ *) % 10.25/10.39 assert (zenon_L428_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.25/10.39 do 0 intro. intros zenon_H18a zenon_H1f3 zenon_H1ef zenon_H94 zenon_H6a zenon_H1b2 zenon_H138 zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_Hb6 zenon_H272 zenon_H12d zenon_H85 zenon_H245 zenon_He9 zenon_H28f zenon_H290 zenon_H16e zenon_Hce zenon_H287 zenon_H2d3 zenon_H29d zenon_Hd5 zenon_H76 zenon_H2cf zenon_H2cd zenon_H298 zenon_H2ae zenon_H15b zenon_H171 zenon_H186 zenon_H17e zenon_Hca zenon_H91 zenon_H289 zenon_Hf4 zenon_H99 zenon_H1ed zenon_H104 zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H128 zenon_H145 zenon_H159 zenon_H157 zenon_H24b zenon_He6 zenon_Ha5 zenon_H269 zenon_H1cb zenon_Hb9 zenon_H1ee. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.25/10.39 apply (zenon_L399_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.25/10.39 apply (zenon_L71_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.25/10.39 apply (zenon_L423_); trivial. % 10.25/10.39 apply (zenon_L427_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.25/10.39 apply (zenon_L111_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.25/10.39 apply (zenon_L219_); trivial. % 10.25/10.39 apply (zenon_L427_); trivial. % 10.25/10.39 (* end of lemma zenon_L428_ *) % 10.25/10.39 assert (zenon_L429_ : (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.39 do 0 intro. intros zenon_H1ee zenon_Hb9 zenon_H1cb zenon_H269 zenon_Ha5 zenon_He6 zenon_H24b zenon_H157 zenon_H159 zenon_H145 zenon_H1de zenon_H26e zenon_Hc0 zenon_H135 zenon_H1f zenon_H28c zenon_H5a zenon_H130 zenon_H2c5 zenon_H104 zenon_H99 zenon_Hf4 zenon_H289 zenon_H91 zenon_Hca zenon_H17e zenon_H186 zenon_H171 zenon_H15b zenon_H2ae zenon_H298 zenon_H2cd zenon_H2cf zenon_Hd5 zenon_H29d zenon_H2d3 zenon_H287 zenon_Hce zenon_H16e zenon_H290 zenon_H28f zenon_H245 zenon_H85 zenon_H12d zenon_H272 zenon_Hb6 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H18d zenon_H138 zenon_H1b2 zenon_H6a zenon_H94 zenon_H1ef zenon_H1f3 zenon_H18a zenon_H1ed zenon_He9 zenon_H76. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.39 apply (zenon_L81_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.39 apply (zenon_L428_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.39 apply (zenon_L185_); trivial. % 10.25/10.39 exact (zenon_H76 zenon_H79). % 10.25/10.39 (* end of lemma zenon_L429_ *) % 10.25/10.39 assert (zenon_L430_ : (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.39 do 0 intro. intros zenon_He9 zenon_H1ed zenon_H18a zenon_H1f3 zenon_H1ef zenon_H94 zenon_H6a zenon_H1b2 zenon_H138 zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_Hb6 zenon_H272 zenon_H12d zenon_H85 zenon_H245 zenon_H290 zenon_H16e zenon_Hce zenon_H287 zenon_H2d3 zenon_H29d zenon_Hd5 zenon_H2cf zenon_H2cd zenon_H298 zenon_H2ae zenon_H15b zenon_H171 zenon_H186 zenon_H17e zenon_Hca zenon_H91 zenon_H289 zenon_Hf4 zenon_H99 zenon_H104 zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H145 zenon_H159 zenon_H157 zenon_H24b zenon_He6 zenon_H269 zenon_H1cb zenon_Hb9 zenon_H1ee zenon_H74 zenon_H28f zenon_H76. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.39 apply (zenon_L16_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.39 apply (zenon_L429_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.39 apply (zenon_L412_); trivial. % 10.25/10.39 exact (zenon_H76 zenon_H79). % 10.25/10.39 (* end of lemma zenon_L430_ *) % 10.25/10.39 assert (zenon_L431_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.39 do 0 intro. intros zenon_H272 zenon_H5b zenon_H17c zenon_H1ed zenon_He9 zenon_H28f zenon_H145 zenon_H128 zenon_H1de zenon_H26e zenon_H290 zenon_H16e zenon_Hce zenon_H287 zenon_H6a zenon_H138 zenon_H2d3 zenon_H104 zenon_H29d zenon_Hd5 zenon_H1ee zenon_He6 zenon_H2cf zenon_H2cd zenon_H298 zenon_Hb9 zenon_H135 zenon_H5a zenon_H130 zenon_H1f zenon_H47 zenon_H2ae zenon_H76. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.39 apply (zenon_L16_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.39 apply (zenon_L119_); trivial. % 10.25/10.39 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.39 apply (zenon_L415_); trivial. % 10.25/10.39 exact (zenon_H76 zenon_H79). % 10.25/10.39 (* end of lemma zenon_L431_ *) % 10.25/10.39 assert (zenon_L432_ : ((op (e1) (e2)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (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))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H9a zenon_H18a zenon_H1f3 zenon_H1ef zenon_H94 zenon_H1b2 zenon_H18d zenon_H37 zenon_H202 zenon_Hfd zenon_Hb6 zenon_H12d zenon_H85 zenon_H245 zenon_H15b zenon_H171 zenon_H17e zenon_Hca zenon_H91 zenon_H289 zenon_Hf4 zenon_H99 zenon_H2c5 zenon_H28c zenon_Hc0 zenon_H157 zenon_H24b zenon_H269 zenon_H1cb zenon_H27c zenon_H186 zenon_H272 zenon_H5b zenon_H1ed zenon_He9 zenon_H28f zenon_H145 zenon_H128 zenon_H1de zenon_H26e zenon_H290 zenon_H16e zenon_Hce zenon_H287 zenon_H6a zenon_H138 zenon_H2d3 zenon_H104 zenon_H29d zenon_Hd5 zenon_H1ee zenon_He6 zenon_H2cf zenon_H2cd zenon_H298 zenon_Hb9 zenon_H135 zenon_H5a zenon_H130 zenon_H1f zenon_H47 zenon_H2ae zenon_H76. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.40 apply (zenon_L359_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.25/10.40 apply (zenon_L44_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.25/10.40 apply (zenon_L425_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.25/10.40 apply (zenon_L384_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.25/10.40 apply (zenon_L257_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.25/10.40 apply (zenon_L319_); trivial. % 10.25/10.40 apply (zenon_L430_); trivial. % 10.25/10.40 apply (zenon_L414_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.40 apply (zenon_L249_); trivial. % 10.25/10.40 apply (zenon_L431_); trivial. % 10.25/10.40 (* end of lemma zenon_L432_ *) % 10.25/10.40 assert (zenon_L433_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H2ae zenon_H47 zenon_H1f zenon_H130 zenon_H5a zenon_H135 zenon_Hb9 zenon_H298 zenon_H2cd zenon_H2cf zenon_He6 zenon_H1ee zenon_Hd5 zenon_H29d zenon_H104 zenon_H2d3 zenon_H138 zenon_H6a zenon_H287 zenon_Hce zenon_H16e zenon_H290 zenon_H26e zenon_H1de zenon_H145 zenon_H28f zenon_H5b zenon_H272 zenon_H186 zenon_H27c zenon_H1cb zenon_H269 zenon_H24b zenon_H157 zenon_Hc0 zenon_H28c zenon_H2c5 zenon_H99 zenon_Hf4 zenon_H289 zenon_H91 zenon_Hca zenon_H17e zenon_H171 zenon_H15b zenon_H245 zenon_H85 zenon_H12d zenon_Hb6 zenon_Hfd zenon_H202 zenon_H37 zenon_H18d zenon_H1b2 zenon_H94 zenon_H1ef zenon_H1f3 zenon_H18a zenon_H9a zenon_H1ed zenon_He9 zenon_H76. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.40 apply (zenon_L81_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.40 apply (zenon_L432_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.40 apply (zenon_L185_); trivial. % 10.25/10.40 exact (zenon_H76 zenon_H79). % 10.25/10.40 (* end of lemma zenon_L433_ *) % 10.25/10.40 assert (zenon_L434_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 10.25/10.40 do 0 intro. intros zenon_H18a zenon_H29d zenon_H17c zenon_H1ee zenon_H26e zenon_H76 zenon_H2cf zenon_H99 zenon_H128 zenon_H1ed zenon_H104 zenon_He6 zenon_H198. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.25/10.40 apply (zenon_L396_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.25/10.40 apply (zenon_L111_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.25/10.40 apply (zenon_L219_); trivial. % 10.25/10.40 apply (zenon_L140_); trivial. % 10.25/10.40 (* end of lemma zenon_L434_ *) % 10.25/10.40 assert (zenon_L435_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H245 zenon_H1f zenon_H130 zenon_H198 zenon_He6 zenon_H104 zenon_H99 zenon_H2cf zenon_H26e zenon_H1ee zenon_H17c zenon_H29d zenon_H18a zenon_H1ed zenon_He9 zenon_H76. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.40 apply (zenon_L81_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.40 apply (zenon_L434_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.40 apply (zenon_L185_); trivial. % 10.25/10.40 exact (zenon_H76 zenon_H79). % 10.25/10.40 (* end of lemma zenon_L435_ *) % 10.25/10.40 assert (zenon_L436_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H18a zenon_H9a zenon_Hfc zenon_Hfd zenon_H158 zenon_Hf4 zenon_H2d3 zenon_H29d zenon_Hd5 zenon_He6 zenon_H76 zenon_H2cf zenon_H2cd zenon_H298 zenon_H14b zenon_H1ed zenon_H104 zenon_H2db zenon_Hb9 zenon_H85 zenon_Hc7 zenon_H2d6 zenon_Hf6 zenon_H100 zenon_H154 zenon_H171 zenon_Ha2 zenon_H145 zenon_H128 zenon_H1de zenon_H26e zenon_Hc0 zenon_H135 zenon_H1f zenon_H28c zenon_H5a zenon_H130 zenon_H2c5 zenon_Hcd zenon_H27c zenon_H1ee. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.25/10.40 apply (zenon_L399_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.25/10.40 apply (zenon_L375_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.25/10.40 apply (zenon_L64_); trivial. % 10.25/10.40 apply (zenon_L406_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.25/10.40 apply (zenon_L124_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.25/10.40 apply (zenon_L219_); trivial. % 10.25/10.40 apply (zenon_L406_); trivial. % 10.25/10.40 (* end of lemma zenon_L436_ *) % 10.25/10.40 assert (zenon_L437_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H272 zenon_He9 zenon_H1cb zenon_H17e zenon_H6a zenon_Hc4 zenon_H186 zenon_H24b zenon_H99 zenon_H1ee zenon_H27c zenon_Hcd zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H128 zenon_H145 zenon_Ha2 zenon_H171 zenon_H154 zenon_H100 zenon_Hf6 zenon_H2d6 zenon_H85 zenon_Hb9 zenon_H2db zenon_H104 zenon_H1ed zenon_H14b zenon_H298 zenon_H2cd zenon_H2cf zenon_He6 zenon_Hd5 zenon_H29d zenon_H2d3 zenon_Hf4 zenon_H158 zenon_Hfd zenon_Hfc zenon_H9a zenon_H18a zenon_H76. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.40 apply (zenon_L324_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.40 apply (zenon_L411_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.40 apply (zenon_L436_); trivial. % 10.25/10.40 exact (zenon_H76 zenon_H79). % 10.25/10.40 (* end of lemma zenon_L437_ *) % 10.25/10.40 assert (zenon_L438_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.25/10.40 do 0 intro. intros zenon_H2ae zenon_H47 zenon_H158 zenon_H157 zenon_H18a zenon_Hfd zenon_Hf4 zenon_H2d3 zenon_H29d zenon_Hd5 zenon_He6 zenon_H76 zenon_H2cf zenon_H2cd zenon_H298 zenon_H14b zenon_H104 zenon_H2db zenon_Hb9 zenon_H85 zenon_H2d6 zenon_Hf6 zenon_H100 zenon_H154 zenon_H171 zenon_Ha2 zenon_H145 zenon_H128 zenon_H1de zenon_H26e zenon_Hc0 zenon_H135 zenon_H1f zenon_H28c zenon_H5a zenon_H130 zenon_H2c5 zenon_Hcd zenon_H27c zenon_H1ee zenon_H15b zenon_Hc7 zenon_H28f zenon_He9 zenon_H1ed. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.25/10.40 apply (zenon_L11_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.25/10.40 apply (zenon_L92_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.25/10.40 apply (zenon_L257_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.25/10.40 apply (zenon_L436_); trivial. % 10.25/10.40 apply (zenon_L94_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.25/10.40 apply (zenon_L412_); trivial. % 10.25/10.40 apply (zenon_L185_); trivial. % 10.25/10.40 (* end of lemma zenon_L438_ *) % 10.25/10.40 assert (zenon_L439_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 10.25/10.40 do 0 intro. intros zenon_H12d zenon_H37 zenon_H91 zenon_H245 zenon_H94 zenon_He9 zenon_H28f zenon_H15b zenon_H1ee zenon_H27c zenon_Hcd zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H145 zenon_H171 zenon_H154 zenon_H100 zenon_Hf6 zenon_H2d6 zenon_H85 zenon_Hb9 zenon_H2db zenon_H104 zenon_H14b zenon_H298 zenon_H2cd zenon_H2cf zenon_H76 zenon_He6 zenon_Hd5 zenon_H29d zenon_H2d3 zenon_Hf4 zenon_Hfd zenon_H18a zenon_H157 zenon_H47 zenon_H2ae zenon_H9a zenon_H99 zenon_H6a zenon_H17e zenon_H1cb zenon_H272 zenon_Hca zenon_H186 zenon_H1ed zenon_H24b zenon_H158. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.40 apply (zenon_L7_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.40 apply (zenon_L247_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.40 apply (zenon_L359_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.25/10.40 apply (zenon_L92_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.25/10.40 apply (zenon_L257_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.40 apply (zenon_L81_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.40 apply (zenon_L437_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.40 apply (zenon_L185_); trivial. % 10.25/10.40 exact (zenon_H76 zenon_H79). % 10.25/10.40 apply (zenon_L94_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.40 apply (zenon_L249_); trivial. % 10.25/10.40 apply (zenon_L253_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.40 apply (zenon_L248_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.25/10.40 apply (zenon_L44_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.25/10.40 apply (zenon_L384_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.25/10.40 apply (zenon_L257_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.25/10.40 apply (zenon_L437_); trivial. % 10.25/10.40 apply (zenon_L94_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.25/10.40 apply (zenon_L418_); trivial. % 10.25/10.40 apply (zenon_L438_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.40 apply (zenon_L249_); trivial. % 10.25/10.40 apply (zenon_L253_); trivial. % 10.25/10.40 (* end of lemma zenon_L439_ *) % 10.25/10.40 assert (zenon_L440_ : ((op (e2) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H103 zenon_H278 zenon_H269 zenon_Hc7 zenon_H17c zenon_H128 zenon_H12d zenon_H37 zenon_H91 zenon_H245 zenon_H94 zenon_He9 zenon_H28f zenon_H15b zenon_H1ee zenon_H27c zenon_Hcd zenon_H2c5 zenon_H130 zenon_H5a zenon_H28c zenon_H1f zenon_H135 zenon_Hc0 zenon_H26e zenon_H1de zenon_H145 zenon_H171 zenon_H154 zenon_H100 zenon_Hf6 zenon_H2d6 zenon_H85 zenon_Hb9 zenon_H2db zenon_H104 zenon_H14b zenon_H298 zenon_H2cd zenon_H2cf zenon_H76 zenon_He6 zenon_Hd5 zenon_H29d zenon_H2d3 zenon_Hf4 zenon_Hfd zenon_H18a zenon_H157 zenon_H47 zenon_H2ae zenon_H9a zenon_H99 zenon_H6a zenon_H17e zenon_H1cb zenon_H272 zenon_Hca zenon_H186 zenon_H1ed zenon_H24b. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.25/10.40 apply (zenon_L396_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.25/10.40 apply (zenon_L124_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.25/10.40 apply (zenon_L245_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H56 | zenon_intro zenon_H26a ]. % 10.25/10.40 apply (zenon_L209_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H198 | zenon_intro zenon_H26b ]. % 10.25/10.40 apply (zenon_L435_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_He5 | zenon_intro zenon_H158 ]. % 10.25/10.40 apply (zenon_L386_); trivial. % 10.25/10.40 apply (zenon_L439_); trivial. % 10.25/10.40 (* end of lemma zenon_L440_ *) % 10.25/10.40 assert (zenon_L441_ : (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H5b zenon_H24b zenon_H1ed zenon_H186 zenon_Hca zenon_H272 zenon_H1cb zenon_H17e zenon_H6a zenon_H99 zenon_H9a zenon_H2ae zenon_H47 zenon_H157 zenon_H18a zenon_Hfd zenon_Hf4 zenon_H2d3 zenon_H29d zenon_Hd5 zenon_He6 zenon_H2cf zenon_H2cd zenon_H298 zenon_H14b zenon_H104 zenon_H2db zenon_Hb9 zenon_H85 zenon_H2d6 zenon_Hf6 zenon_H100 zenon_H154 zenon_H171 zenon_H145 zenon_H1de zenon_H26e zenon_Hc0 zenon_H135 zenon_H1f zenon_H28c zenon_H5a zenon_H130 zenon_H2c5 zenon_Hcd zenon_H27c zenon_H1ee zenon_H15b zenon_H28f zenon_He9 zenon_H94 zenon_H245 zenon_H91 zenon_H37 zenon_H12d zenon_H128 zenon_H17c zenon_H269 zenon_H278 zenon_H103 zenon_H76. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.40 apply (zenon_L16_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.40 apply (zenon_L119_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.40 apply (zenon_L440_); trivial. % 10.25/10.40 exact (zenon_H76 zenon_H79). % 10.25/10.40 (* end of lemma zenon_L441_ *) % 10.25/10.40 assert (zenon_L442_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H74 zenon_H103 zenon_H99. % 10.25/10.40 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H98 ]. % 10.25/10.40 cut (((e1) = (e1)) = ((e0) = (e1))). % 10.25/10.40 intro zenon_D_pnotp. % 10.25/10.40 apply zenon_H99. % 10.25/10.40 rewrite <- zenon_D_pnotp. % 10.25/10.40 exact zenon_Hf7. % 10.25/10.40 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.25/10.40 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 10.25/10.40 congruence. % 10.25/10.40 cut (((op (e2) (e2)) = (e0)) = ((e1) = (e0))). % 10.25/10.40 intro zenon_D_pnotp. % 10.25/10.40 apply zenon_Hf8. % 10.25/10.40 rewrite <- zenon_D_pnotp. % 10.25/10.40 exact zenon_H74. % 10.25/10.40 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.40 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 10.25/10.40 congruence. % 10.25/10.40 exact (zenon_H163 zenon_H103). % 10.25/10.40 apply zenon_H84. apply refl_equal. % 10.25/10.40 apply zenon_H98. apply refl_equal. % 10.25/10.40 apply zenon_H98. apply refl_equal. % 10.25/10.40 (* end of lemma zenon_L442_ *) % 10.25/10.40 assert (zenon_L443_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H124 zenon_H99 zenon_H74 zenon_H2db zenon_Hf4 zenon_H2d6 zenon_Hf6 zenon_H100 zenon_H154 zenon_H171 zenon_Ha2 zenon_H289 zenon_H76 zenon_He9 zenon_H1ed zenon_H2cf zenon_H28c zenon_H135 zenon_H26e zenon_H145 zenon_H1f3 zenon_H2cd zenon_H245 zenon_H104 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6a zenon_H94 zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef zenon_H2c5 zenon_Hcd zenon_H27c zenon_H1ee. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.40 apply (zenon_L59_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.40 apply (zenon_L61_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.40 apply (zenon_L442_); trivial. % 10.25/10.40 apply (zenon_L402_); trivial. % 10.25/10.40 (* end of lemma zenon_L443_ *) % 10.25/10.40 assert (zenon_L444_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H18a zenon_H29d zenon_H17c zenon_H1ee zenon_H26e zenon_H76 zenon_H2cf zenon_H99 zenon_H128 zenon_H1ed zenon_H104 zenon_H107 zenon_Hd5. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.25/10.40 apply (zenon_L396_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.25/10.40 apply (zenon_L111_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.25/10.40 apply (zenon_L219_); trivial. % 10.25/10.40 apply (zenon_L126_); trivial. % 10.25/10.40 (* end of lemma zenon_L444_ *) % 10.25/10.40 assert (zenon_L445_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H17e zenon_H1ee zenon_H27c zenon_Hcd zenon_H2c5 zenon_H1ef zenon_Hb9 zenon_Hc0 zenon_H1de zenon_H94 zenon_H6a zenon_H1cb zenon_H130 zenon_H1b2 zenon_H138 zenon_H18d zenon_H1f zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_Hfd zenon_H104 zenon_H245 zenon_H2cd zenon_H1f3 zenon_H145 zenon_H26e zenon_H135 zenon_H28c zenon_H2cf zenon_H1ed zenon_H76 zenon_H289 zenon_H171 zenon_H154 zenon_H100 zenon_Hf6 zenon_H2d6 zenon_Hf4 zenon_H2db zenon_H18a zenon_H99 zenon_H2d3 zenon_H29d zenon_Hd5 zenon_He6 zenon_H298 zenon_H14b zenon_H278 zenon_H85 zenon_H5a zenon_H124 zenon_Hca zenon_H91 zenon_H128 zenon_Ha5 zenon_He9. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.40 apply (zenon_L248_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.25/10.40 apply (zenon_L417_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.40 apply (zenon_L59_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.40 apply (zenon_L61_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.40 apply (zenon_L405_); trivial. % 10.25/10.40 apply (zenon_L402_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.25/10.40 apply (zenon_L443_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.40 apply (zenon_L59_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.40 apply (zenon_L61_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.25/10.40 apply (zenon_L403_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.25/10.40 apply (zenon_L124_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.25/10.40 apply (zenon_L245_); trivial. % 10.25/10.40 apply (zenon_L406_); trivial. % 10.25/10.40 apply (zenon_L402_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.40 apply (zenon_L372_); trivial. % 10.25/10.40 apply (zenon_L119_); trivial. % 10.25/10.40 (* end of lemma zenon_L445_ *) % 10.25/10.40 assert (zenon_L446_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (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 (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.25/10.40 do 0 intro. intros zenon_H1a3 zenon_Hb6 zenon_H272 zenon_H12d zenon_H28f zenon_H15b zenon_H27c zenon_H2c5 zenon_H171 zenon_H154 zenon_H100 zenon_Hf6 zenon_H2d6 zenon_H85 zenon_H2db zenon_H14b zenon_H298 zenon_He6 zenon_Hd5 zenon_H29d zenon_H2d3 zenon_Hf4 zenon_H18a zenon_H157 zenon_H2ae zenon_H99 zenon_H24b zenon_H17e zenon_H186 zenon_Hca zenon_H91 zenon_H269 zenon_H293 zenon_H290 zenon_Hce zenon_H287 zenon_H90 zenon_H124 zenon_H278 zenon_H15e zenon_H289 zenon_H76 zenon_He9 zenon_H1ed zenon_H2cf zenon_H28c zenon_H135 zenon_H26e zenon_H145 zenon_H1ee zenon_H1f3 zenon_H2cd zenon_H245 zenon_H104 zenon_Hfd zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H6a zenon_H94 zenon_H1de zenon_Hc0 zenon_Hb9 zenon_H1ef. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.40 apply (zenon_L88_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.40 apply (zenon_L89_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.25/10.40 apply (zenon_L394_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.25/10.40 apply (zenon_L247_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.40 apply (zenon_L58_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.40 apply (zenon_L247_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.40 apply (zenon_L248_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.40 apply (zenon_L59_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.40 apply (zenon_L61_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.40 apply (zenon_L81_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.40 apply (zenon_L408_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.40 apply (zenon_L185_); trivial. % 10.25/10.40 exact (zenon_H76 zenon_H79). % 10.25/10.40 apply (zenon_L402_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.40 apply (zenon_L249_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.25/10.40 apply (zenon_L433_); trivial. % 10.25/10.40 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.25/10.40 exact (zenon_H90 zenon_H8b). % 10.25/10.41 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.41 apply (zenon_L81_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.41 apply (zenon_L441_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.41 apply (zenon_L185_); trivial. % 10.25/10.41 exact (zenon_H76 zenon_H79). % 10.25/10.41 apply (zenon_L219_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.41 apply (zenon_L359_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.25/10.41 apply (zenon_L44_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.41 apply (zenon_L59_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.41 apply (zenon_L61_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.41 apply (zenon_L408_); trivial. % 10.25/10.41 apply (zenon_L402_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.25/10.41 apply (zenon_L443_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.41 apply (zenon_L59_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.41 apply (zenon_L61_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.41 apply (zenon_L407_); trivial. % 10.25/10.41 apply (zenon_L402_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.41 apply (zenon_L372_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.41 apply (zenon_L59_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.41 apply (zenon_L61_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.41 apply (zenon_L441_); trivial. % 10.25/10.41 apply (zenon_L444_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.41 apply (zenon_L81_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.41 apply (zenon_L445_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.41 apply (zenon_L185_); trivial. % 10.25/10.41 exact (zenon_H76 zenon_H79). % 10.25/10.41 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.41 apply (zenon_L99_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.41 apply (zenon_L91_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.25/10.41 apply (zenon_L33_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.25/10.41 apply (zenon_L247_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.25/10.41 apply (zenon_L439_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.41 apply (zenon_L58_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.41 apply (zenon_L247_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.41 apply (zenon_L420_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.41 apply (zenon_L359_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.25/10.41 apply (zenon_L417_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.25/10.41 apply (zenon_L420_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.25/10.41 apply (zenon_L418_); trivial. % 10.25/10.41 apply (zenon_L438_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.41 apply (zenon_L372_); trivial. % 10.25/10.41 apply (zenon_L119_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.25/10.41 apply (zenon_L248_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.25/10.41 apply (zenon_L92_); trivial. % 10.25/10.41 apply (zenon_L176_); trivial. % 10.25/10.41 apply (zenon_L391_); trivial. % 10.25/10.41 (* end of lemma zenon_L446_ *) % 10.25/10.41 assert (zenon_L447_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.41 do 0 intro. intros zenon_H245 zenon_H133 zenon_H2c5 zenon_Hfd zenon_H158 zenon_Hf4 zenon_Hef zenon_H85 zenon_H1ee zenon_H2ab zenon_H24b zenon_H91 zenon_H104 zenon_H17e zenon_H1f3 zenon_H90 zenon_H99 zenon_H272 zenon_H1ed zenon_He9 zenon_H76. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.41 apply (zenon_L110_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.41 apply (zenon_L376_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.41 apply (zenon_L185_); trivial. % 10.25/10.41 exact (zenon_H76 zenon_H79). % 10.25/10.41 (* end of lemma zenon_L447_ *) % 10.25/10.41 assert (zenon_L448_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.41 do 0 intro. intros zenon_H186 zenon_H245 zenon_H133 zenon_H2c5 zenon_Hfd zenon_H158 zenon_Hf4 zenon_H85 zenon_H1ee zenon_H2ab zenon_H24b zenon_H91 zenon_H104 zenon_H17e zenon_H1f3 zenon_H90 zenon_H99 zenon_H272 zenon_H1ed zenon_He9 zenon_H76. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.41 apply (zenon_L254_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.41 apply (zenon_L369_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.41 exact (zenon_H90 zenon_H8b). % 10.25/10.41 apply (zenon_L447_); trivial. % 10.25/10.41 (* end of lemma zenon_L448_ *) % 10.25/10.41 assert (zenon_L449_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.41 do 0 intro. intros zenon_H15e zenon_H1f zenon_Hf6 zenon_H27c zenon_H186 zenon_H245 zenon_H133 zenon_H2c5 zenon_Hfd zenon_Hf4 zenon_H85 zenon_H1ee zenon_H2ab zenon_H24b zenon_H91 zenon_H104 zenon_H17e zenon_H1f3 zenon_H90 zenon_H99 zenon_H272 zenon_H1ed zenon_He9 zenon_H76. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.41 apply (zenon_L54_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.41 apply (zenon_L99_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.41 apply (zenon_L252_); trivial. % 10.25/10.41 apply (zenon_L448_); trivial. % 10.25/10.41 (* end of lemma zenon_L449_ *) % 10.25/10.41 assert (zenon_L450_ : (~((op (e1) (e1)) = (e0))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (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 (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.41 do 0 intro. intros zenon_H6b zenon_H29b zenon_Hc6 zenon_H284 zenon_H281 zenon_H29c zenon_Hdf zenon_Hda zenon_H191 zenon_H182 zenon_H177 zenon_H1a2 zenon_H13d zenon_Hbb zenon_H142 zenon_H1ef zenon_Hc0 zenon_H1de zenon_H94 zenon_H1cb zenon_H130 zenon_H1b2 zenon_H138 zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_H2cd zenon_H145 zenon_H26e zenon_H135 zenon_H28c zenon_H2cf zenon_H289 zenon_H278 zenon_H124 zenon_H287 zenon_Hce zenon_H290 zenon_H293 zenon_H269 zenon_Hca zenon_H2ae zenon_H157 zenon_H18a zenon_H2d3 zenon_H29d zenon_Hd5 zenon_He6 zenon_H298 zenon_H14b zenon_H2db zenon_H2d6 zenon_H100 zenon_H154 zenon_H171 zenon_H15b zenon_H28f zenon_H12d zenon_Hb6 zenon_H1a3 zenon_Hb9 zenon_H15e zenon_H1f zenon_Hf6 zenon_H27c zenon_H186 zenon_H245 zenon_H2c5 zenon_Hfd zenon_Hf4 zenon_H85 zenon_H1ee zenon_H2ab zenon_H24b zenon_H91 zenon_H104 zenon_H17e zenon_H1f3 zenon_H90 zenon_H99 zenon_H272 zenon_H1ed zenon_He9 zenon_H76. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.41 apply (zenon_L57_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.41 apply (zenon_L89_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.41 apply (zenon_L379_); trivial. % 10.25/10.41 apply (zenon_L393_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.25/10.41 apply (zenon_L446_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.25/10.41 apply (zenon_L59_); trivial. % 10.25/10.41 apply (zenon_L449_); trivial. % 10.25/10.41 (* end of lemma zenon_L450_ *) % 10.25/10.41 assert (zenon_L451_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.41 do 0 intro. intros zenon_H29b zenon_H202 zenon_H15e zenon_H27c zenon_Hb6 zenon_H18a zenon_H278 zenon_H13d zenon_H1a3 zenon_H157 zenon_Hda zenon_Hc6 zenon_Hdf zenon_H124 zenon_Hd5 zenon_Hbb zenon_H94 zenon_H138 zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H1f zenon_H135 zenon_H171 zenon_Hca zenon_H284 zenon_H28c zenon_H1ef zenon_H1de zenon_H1cb zenon_H289 zenon_H287 zenon_H290 zenon_H28f zenon_H293 zenon_H269 zenon_He6 zenon_H298 zenon_H15b zenon_Hc0 zenon_H281 zenon_H1b2 zenon_H130 zenon_H29c zenon_H6b zenon_H16e zenon_H186 zenon_H245 zenon_H133 zenon_H2c5 zenon_Hfd zenon_Hf4 zenon_H85 zenon_H1ee zenon_H2ab zenon_H24b zenon_H91 zenon_H104 zenon_H17e zenon_H1f3 zenon_H90 zenon_H99 zenon_H272 zenon_H1ed zenon_He9 zenon_H76. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.41 apply (zenon_L54_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.41 apply (zenon_L371_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.41 apply (zenon_L105_); trivial. % 10.25/10.41 apply (zenon_L448_); trivial. % 10.25/10.41 (* end of lemma zenon_L451_ *) % 10.25/10.41 assert (zenon_L452_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 10.25/10.41 do 0 intro. intros zenon_H18a zenon_H2cd zenon_H2cf zenon_H76 zenon_H1ee zenon_Hd5 zenon_H26e zenon_H29d zenon_H2d3 zenon_H99 zenon_H128 zenon_H1ed zenon_H104 zenon_He6 zenon_H198. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.25/10.41 apply (zenon_L399_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.25/10.41 apply (zenon_L111_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.25/10.41 apply (zenon_L219_); trivial. % 10.25/10.41 apply (zenon_L140_); trivial. % 10.25/10.41 (* end of lemma zenon_L452_ *) % 10.25/10.41 assert (zenon_L453_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.41 do 0 intro. intros zenon_H245 zenon_H1f zenon_H130 zenon_H198 zenon_He6 zenon_H104 zenon_H99 zenon_H2d3 zenon_H29d zenon_H26e zenon_Hd5 zenon_H1ee zenon_H2cf zenon_H2cd zenon_H18a zenon_H1ed zenon_He9 zenon_H76. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.41 apply (zenon_L81_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.41 apply (zenon_L452_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.41 apply (zenon_L185_); trivial. % 10.25/10.41 exact (zenon_H76 zenon_H79). % 10.25/10.41 (* end of lemma zenon_L453_ *) % 10.25/10.41 assert (zenon_L454_ : ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = 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(e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.25/10.41 do 0 intro. intros zenon_H1f zenon_H37 zenon_H47 zenon_H5b zenon_Hb9 zenon_H85 zenon_He9 zenon_H289 zenon_H191 zenon_H18d zenon_Hc0 zenon_H100 zenon_H182 zenon_Hd5 zenon_H124 zenon_H15e zenon_He6 zenon_H1a3 zenon_H1a2 zenon_H14b zenon_H12d zenon_H18a zenon_H17e zenon_H177 zenon_H142 zenon_Hfd zenon_H186 zenon_H13d zenon_H104 zenon_H145 zenon_H26e zenon_H135 zenon_H244 zenon_H130 zenon_H2b9 zenon_Hdf zenon_Hda zenon_Hbb zenon_H94 zenon_H6b zenon_H99 zenon_Hb3 zenon_H9c zenon_Hb6 zenon_Hf4 zenon_H1b2 zenon_H138 zenon_H115 zenon_Hc6 zenon_He0 zenon_H15b zenon_H157 zenon_H154 zenon_H12a zenon_H173 zenon_H171 zenon_H1cb zenon_H1de zenon_H1ef zenon_H202 zenon_H245 zenon_H24e zenon_H24b zenon_H2ae zenon_H27c zenon_H262 zenon_H2bc zenon_H278 zenon_H28c zenon_H287 zenon_H290 zenon_H293 zenon_H2ab zenon_Hce zenon_H2c5 zenon_H29c zenon_H281 zenon_H298 zenon_H269 zenon_H28f zenon_H284 zenon_Hca zenon_H272 zenon_H29b zenon_H2d6 zenon_H2db zenon_H29d zenon_H2d3 zenon_H2cf zenon_H2cd. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H29c); [ zenon_intro zenon_H76 | zenon_intro zenon_H13b ]. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.25/10.41 apply (zenon_L1_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.25/10.41 apply (zenon_L2_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.25/10.41 apply (zenon_L3_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.25/10.41 apply (zenon_L4_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.25/10.41 apply (zenon_L5_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.25/10.41 apply (zenon_L6_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.25/10.41 apply (zenon_L8_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.25/10.41 apply (zenon_L9_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.25/10.41 apply (zenon_L10_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.25/10.41 apply (zenon_L12_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.25/10.41 apply (zenon_L13_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.25/10.41 apply (zenon_L14_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.25/10.41 apply (zenon_L15_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.25/10.41 apply (zenon_L17_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.25/10.41 apply (zenon_L18_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.25/10.41 apply (zenon_L19_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.25/10.41 apply (zenon_L20_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.25/10.41 apply (zenon_L21_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.25/10.41 apply (zenon_L112_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.25/10.41 apply (zenon_L23_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.25/10.41 apply (zenon_L24_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.25/10.41 apply (zenon_L25_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.25/10.41 apply (zenon_L26_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.25/10.41 apply (zenon_L27_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.25/10.41 apply (zenon_L30_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.25/10.41 apply (zenon_L31_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.25/10.41 apply (zenon_L32_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.25/10.41 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H8b. zenon_intro zenon_H190. % 10.25/10.41 apply (zenon_and_s _ _ zenon_H190). zenon_intro zenon_H8c. zenon_intro zenon_H1c8. % 10.25/10.41 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.41 apply (zenon_L57_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.41 apply (zenon_L42_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.41 apply (zenon_L349_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.41 apply (zenon_L54_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.25/10.41 apply (zenon_L54_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.25/10.41 apply (zenon_L352_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.25/10.41 apply (zenon_L354_); trivial. % 10.25/10.41 apply (zenon_L144_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.25/10.41 apply (zenon_L355_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.25/10.41 apply (zenon_L352_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.25/10.41 apply (zenon_L92_); trivial. % 10.25/10.41 apply (zenon_L356_); trivial. % 10.25/10.41 apply (zenon_L103_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.25/10.41 apply (zenon_L33_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.25/10.41 exact (zenon_H6b zenon_H6f). % 10.25/10.41 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.25/10.41 apply (zenon_L35_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.41 apply (zenon_L41_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.41 exact (zenon_H8c zenon_H91). % 10.25/10.41 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.41 apply (zenon_L152_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.41 apply (zenon_L59_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.41 apply (zenon_L61_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.41 apply (zenon_L122_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.25/10.41 apply (zenon_L127_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.25/10.41 apply (zenon_L199_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.25/10.41 exact (zenon_H1f9 zenon_H1ed). % 10.25/10.41 apply (zenon_L357_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.25/10.41 apply (zenon_L131_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.41 apply (zenon_L29_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.41 apply (zenon_L42_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.41 apply (zenon_L349_); trivial. % 10.25/10.41 apply (zenon_L143_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.25/10.41 apply (zenon_L55_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.25/10.41 apply (zenon_L56_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.25/10.41 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hef. zenon_intro zenon_H170. % 10.25/10.41 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_Ha3. zenon_intro zenon_H1d3. % 10.25/10.41 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.25/10.41 apply (zenon_L192_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.25/10.41 apply (zenon_L147_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.25/10.41 apply (zenon_L148_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.25/10.41 apply (zenon_L149_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.25/10.41 apply (zenon_L150_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.25/10.41 apply (zenon_L206_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.25/10.41 apply (zenon_L153_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.25/10.41 apply (zenon_L154_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.25/10.41 apply (zenon_L155_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.25/10.41 apply (zenon_L156_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.25/10.41 apply (zenon_L157_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.25/10.41 apply (zenon_L158_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.25/10.41 apply (zenon_L159_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.25/10.41 apply (zenon_L160_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.25/10.41 apply (zenon_L233_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.25/10.41 apply (zenon_L163_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.25/10.41 apply (zenon_L164_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.25/10.41 apply (zenon_L165_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.25/10.41 apply (zenon_L166_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.25/10.41 apply (zenon_L167_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.25/10.41 apply (zenon_L168_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.25/10.41 apply (zenon_L169_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.25/10.41 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H127. zenon_intro zenon_H1e2. % 10.25/10.41 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H1e5. zenon_intro zenon_H2e. % 10.25/10.41 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.41 apply (zenon_L88_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.41 apply (zenon_L323_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.41 apply (zenon_L358_); trivial. % 10.25/10.41 apply (zenon_L363_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.25/10.41 apply (zenon_L172_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.25/10.41 apply (zenon_L368_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.25/10.41 apply (zenon_L174_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.25/10.41 apply (zenon_L246_); trivial. % 10.25/10.41 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.25/10.41 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H1ed. zenon_intro zenon_H1f4. % 10.25/10.41 apply (zenon_and_s _ _ zenon_H1f4). zenon_intro zenon_H1ee. zenon_intro zenon_H8f. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.42 apply (zenon_L295_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.42 apply (zenon_L371_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.42 apply (zenon_L252_); trivial. % 10.25/10.42 apply (zenon_L378_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.25/10.42 apply (zenon_L450_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.42 apply (zenon_L54_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.42 apply (zenon_L371_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.42 apply (zenon_L105_); trivial. % 10.25/10.42 apply (zenon_L378_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.25/10.42 apply (zenon_L278_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.25/10.42 apply (zenon_L59_); trivial. % 10.25/10.42 apply (zenon_L451_); trivial. % 10.25/10.42 apply (zenon_L453_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.25/10.42 apply (zenon_L178_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.25/10.42 apply (zenon_L179_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.25/10.42 apply (zenon_L180_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.25/10.42 apply (zenon_L181_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.25/10.42 apply (zenon_L182_); trivial. % 10.25/10.42 apply (zenon_L183_); trivial. % 10.25/10.42 apply (zenon_L184_); trivial. % 10.25/10.42 (* end of lemma zenon_L454_ *) % 10.25/10.42 assert (zenon_L455_ : ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e2)) = (e0))) -> ((op (e2) (e1)) = (e2)) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.25/10.42 do 0 intro. intros zenon_H31 zenon_H71 zenon_Hc3 zenon_Hf6 zenon_H189 zenon_H2cd zenon_H2cf zenon_H2d3 zenon_H29d zenon_H2db zenon_H2d6 zenon_H29b zenon_H272 zenon_Hca zenon_H284 zenon_H28f zenon_H269 zenon_H298 zenon_H281 zenon_H29c zenon_H2c5 zenon_Hce zenon_H2ab zenon_H293 zenon_H290 zenon_H287 zenon_H28c zenon_H278 zenon_H2bc zenon_H262 zenon_H27c zenon_H2ae zenon_H24b zenon_H24e zenon_H245 zenon_H202 zenon_H1ef zenon_H1de zenon_H1cb zenon_H171 zenon_H173 zenon_H12a zenon_H154 zenon_H157 zenon_H15b zenon_He0 zenon_Hc6 zenon_H115 zenon_H138 zenon_H1b2 zenon_Hf4 zenon_Hb6 zenon_H9c zenon_Hb3 zenon_H99 zenon_H6b zenon_H94 zenon_Hbb zenon_Hda zenon_Hdf zenon_H2b9 zenon_H130 zenon_H244 zenon_H135 zenon_H26e zenon_H145 zenon_H104 zenon_H13d zenon_H186 zenon_H142 zenon_H177 zenon_H17e zenon_H18a zenon_H12d zenon_H14b zenon_H1a2 zenon_H1a3 zenon_He6 zenon_H15e zenon_H124 zenon_Hd5 zenon_H182 zenon_H100 zenon_Hc0 zenon_H18d zenon_H191 zenon_H289 zenon_He9 zenon_H85 zenon_H5b zenon_H47 zenon_H37 zenon_H1f zenon_Hfd zenon_H13b. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.42 apply (zenon_L57_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.42 apply (zenon_L348_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.42 apply (zenon_L454_); trivial. % 10.25/10.42 apply (zenon_L255_); trivial. % 10.25/10.42 (* end of lemma zenon_L455_ *) % 10.25/10.42 assert (zenon_L456_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.25/10.42 do 0 intro. intros zenon_H191 zenon_H100 zenon_H182 zenon_H1a2 zenon_H14b zenon_H177 zenon_H142 zenon_H145 zenon_H26e zenon_H244 zenon_H2b9 zenon_Hb3 zenon_H9c zenon_H115 zenon_He0 zenon_H154 zenon_H173 zenon_H245 zenon_H24e zenon_H2ae zenon_H262 zenon_H2bc zenon_Hce zenon_H2c5 zenon_H2d6 zenon_H2db zenon_H2d3 zenon_H2cf zenon_H2cd zenon_H29c zenon_H130 zenon_H1b2 zenon_H15b zenon_H298 zenon_He6 zenon_H269 zenon_H293 zenon_H28f zenon_H290 zenon_H287 zenon_H289 zenon_H1cb zenon_H1de zenon_H1ef zenon_H28c zenon_H284 zenon_H171 zenon_H135 zenon_H47 zenon_H5b zenon_H18d zenon_H138 zenon_Hbb zenon_Hd5 zenon_H124 zenon_H272 zenon_Hdf zenon_Hda zenon_H157 zenon_H1a3 zenon_H13d zenon_H278 zenon_H18a zenon_H186 zenon_H17e zenon_H27c zenon_H24b zenon_H15e zenon_H202 zenon_H29b zenon_Hfd zenon_Hf4 zenon_Hb6 zenon_H94 zenon_H29d zenon_H189 zenon_H99 zenon_H12a zenon_Hf6 zenon_He9 zenon_H2ab zenon_H6b zenon_H37 zenon_H12d zenon_Hca zenon_H1f zenon_Hc0 zenon_Hc3 zenon_H85 zenon_H71 zenon_Hc6 zenon_H281 zenon_H104 zenon_H13b. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.25/10.42 apply (zenon_L455_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.25/10.42 apply (zenon_L278_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.42 apply (zenon_L29_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.42 apply (zenon_L348_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.42 apply (zenon_L59_); trivial. % 10.25/10.42 apply (zenon_L255_); trivial. % 10.25/10.42 apply (zenon_L123_); trivial. % 10.25/10.42 (* end of lemma zenon_L456_ *) % 10.25/10.42 assert (zenon_L457_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.25/10.42 do 0 intro. intros zenon_Hca zenon_H1f zenon_Hc0 zenon_Hc3 zenon_H85 zenon_H71 zenon_H15b zenon_H135 zenon_H13b zenon_H119 zenon_H100 zenon_H16e zenon_H266 zenon_H115 zenon_H36 zenon_He5 zenon_H24b zenon_Hc6. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.25/10.42 apply (zenon_L44_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.25/10.42 apply (zenon_L45_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.25/10.42 exact (zenon_H71 zenon_H74). % 10.25/10.42 apply (zenon_L285_); trivial. % 10.25/10.42 (* end of lemma zenon_L457_ *) % 10.25/10.42 assert (zenon_L458_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> False). % 10.25/10.42 do 0 intro. intros zenon_H12d zenon_He9 zenon_H6b zenon_H2ab zenon_H177 zenon_Hc6 zenon_H24b zenon_He5 zenon_H266 zenon_H100 zenon_H13b zenon_H135 zenon_H15b zenon_H71 zenon_H85 zenon_Hc0 zenon_H1f zenon_Hca zenon_Hda zenon_H16e zenon_H24e zenon_H104 zenon_H119 zenon_H115 zenon_Hc3 zenon_Hf4 zenon_H99. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.42 apply (zenon_L134_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.42 exact (zenon_H6b zenon_H6f). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.42 apply (zenon_L45_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.42 apply (zenon_L283_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.42 apply (zenon_L457_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.42 apply (zenon_L131_); trivial. % 10.25/10.42 apply (zenon_L344_); trivial. % 10.25/10.42 (* end of lemma zenon_L458_ *) % 10.25/10.42 assert (zenon_L459_ : (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 10.25/10.42 do 0 intro. intros zenon_H163 zenon_H281 zenon_H37 zenon_H12a zenon_H29d zenon_H94 zenon_Hb6 zenon_H29b zenon_H202 zenon_H27c zenon_H17e zenon_H186 zenon_H18a zenon_H278 zenon_H13d zenon_H157 zenon_Hdf zenon_H272 zenon_H124 zenon_Hd5 zenon_Hbb zenon_H138 zenon_H18d zenon_H5b zenon_H47 zenon_H171 zenon_H284 zenon_H28c zenon_H1ef zenon_H1de zenon_H1cb zenon_H289 zenon_H287 zenon_H290 zenon_H28f zenon_H293 zenon_H269 zenon_H298 zenon_H1b2 zenon_H130 zenon_H29c zenon_H2cd zenon_H2cf zenon_H2d3 zenon_H2db zenon_H2d6 zenon_H2c5 zenon_Hce zenon_H2bc zenon_H262 zenon_H2ae zenon_H245 zenon_H173 zenon_H154 zenon_He0 zenon_H9c zenon_Hb3 zenon_H2b9 zenon_H244 zenon_H26e zenon_H145 zenon_H142 zenon_H14b zenon_H1a2 zenon_H182 zenon_H191 zenon_Hfd zenon_H104 zenon_H12d zenon_He9 zenon_H6b zenon_H2ab zenon_H177 zenon_Hc6 zenon_H24b zenon_H266 zenon_H100 zenon_H13b zenon_H135 zenon_H15b zenon_H71 zenon_H85 zenon_Hc0 zenon_H1f zenon_Hca zenon_Hda zenon_H24e zenon_H115 zenon_Hc3 zenon_Hf4 zenon_H99 zenon_H15e zenon_H1a3 zenon_He6 zenon_H189. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.42 apply (zenon_L29_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.25/10.42 apply (zenon_L33_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.25/10.42 exact (zenon_H6b zenon_H6f). % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.42 apply (zenon_L236_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.42 apply (zenon_L228_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.42 apply (zenon_L35_); trivial. % 10.25/10.42 apply (zenon_L280_); trivial. % 10.25/10.42 apply (zenon_L47_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.42 apply (zenon_L152_); trivial. % 10.25/10.42 apply (zenon_L255_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.25/10.42 apply (zenon_L456_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.42 apply (zenon_L29_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.42 apply (zenon_L281_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.42 apply (zenon_L189_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.42 apply (zenon_L54_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.42 apply (zenon_L458_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.42 apply (zenon_L105_); trivial. % 10.25/10.42 apply (zenon_L103_); trivial. % 10.25/10.42 apply (zenon_L140_); trivial. % 10.25/10.42 (* end of lemma zenon_L459_ *) % 10.25/10.42 assert (zenon_L460_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (e1))) -> False). % 10.25/10.42 do 0 intro. intros zenon_H2ab zenon_Hf4 zenon_Hba zenon_H104 zenon_Ha2 zenon_H9a zenon_H99 zenon_Hf3. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.42 apply (zenon_L236_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.42 apply (zenon_L225_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.42 apply (zenon_L35_); trivial. % 10.25/10.42 exact (zenon_Hf3 zenon_Hef). % 10.25/10.42 (* end of lemma zenon_L460_ *) % 10.25/10.42 assert (zenon_L461_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.25/10.42 do 0 intro. intros zenon_H2a8 zenon_Hfd zenon_Hcd zenon_H104 zenon_H8b zenon_Hff zenon_H13b zenon_H1ef. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.25/10.42 apply (zenon_L91_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.25/10.42 apply (zenon_L118_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.25/10.42 exact (zenon_Hff zenon_Hfc). % 10.25/10.42 apply (zenon_L176_); trivial. % 10.25/10.42 (* end of lemma zenon_L461_ *) % 10.25/10.42 assert (zenon_L462_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (e1))) -> False). % 10.25/10.42 do 0 intro. intros zenon_H2ab zenon_H99 zenon_Hf4 zenon_Hd4 zenon_H293 zenon_H284 zenon_H135 zenon_H289 zenon_He9 zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H94 zenon_H1de zenon_Hc0 zenon_H287 zenon_Hc4 zenon_H28c zenon_H290 zenon_H71 zenon_H278 zenon_H28f zenon_H1cf zenon_H298 zenon_H85 zenon_Hca zenon_H269 zenon_H24b zenon_He6 zenon_H157 zenon_H272 zenon_H171 zenon_H15b zenon_Ha2 zenon_H1ef zenon_H13b zenon_Hff zenon_H104 zenon_Hcd zenon_Hfd zenon_H2a8 zenon_Hf3. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.42 apply (zenon_L275_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.42 apply (zenon_L225_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.42 apply (zenon_L461_); trivial. % 10.25/10.42 exact (zenon_Hf3 zenon_Hef). % 10.25/10.42 (* end of lemma zenon_L462_ *) % 10.25/10.42 assert (zenon_L463_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.25/10.42 do 0 intro. intros zenon_Hdf zenon_Hf4 zenon_H6a zenon_H1ef zenon_H13b zenon_Hff zenon_H128 zenon_Hfd zenon_H2a8 zenon_Hcd zenon_Hda zenon_Hd4 zenon_Hc6. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.42 apply (zenon_L236_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.25/10.42 apply (zenon_L91_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.25/10.42 apply (zenon_L372_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.25/10.42 exact (zenon_Hff zenon_Hfc). % 10.25/10.42 apply (zenon_L176_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.42 apply (zenon_L50_); trivial. % 10.25/10.42 apply (zenon_L238_); trivial. % 10.25/10.42 (* end of lemma zenon_L463_ *) % 10.25/10.42 assert (zenon_L464_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 10.25/10.42 do 0 intro. intros zenon_H15b zenon_H135 zenon_H13b zenon_Ha2 zenon_H171 zenon_Hff zenon_H157 zenon_H158. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.25/10.42 apply (zenon_L211_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.25/10.42 apply (zenon_L257_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.25/10.42 exact (zenon_Hff zenon_Hfc). % 10.25/10.42 apply (zenon_L94_); trivial. % 10.25/10.42 (* end of lemma zenon_L464_ *) % 10.25/10.42 assert (zenon_L465_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e3))\/(((op (e1) (e3)) = (e3))\/(((op (e2) (e3)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.25/10.42 do 0 intro. intros zenon_H266 zenon_H157 zenon_H15e zenon_H2a8 zenon_H104 zenon_Hdf zenon_Hf4 zenon_Hda zenon_Hc6 zenon_H2ab zenon_H99 zenon_H293 zenon_H284 zenon_H289 zenon_He9 zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H1f zenon_H18d zenon_H138 zenon_H1b2 zenon_H130 zenon_H1cb zenon_H94 zenon_Hc0 zenon_H287 zenon_H28c zenon_H290 zenon_H278 zenon_H28f zenon_H298 zenon_H85 zenon_Hca zenon_H269 zenon_H24b zenon_He6 zenon_H272 zenon_H12d zenon_Hfd zenon_H15b zenon_H135 zenon_H171 zenon_H2cd zenon_H2cf zenon_H2d3 zenon_H29d zenon_H2db zenon_H2d6 zenon_H29b zenon_H281 zenon_H29c zenon_H2c5 zenon_Hce zenon_H2bc zenon_H262 zenon_H27c zenon_H2ae zenon_H24e zenon_H245 zenon_H173 zenon_H12a zenon_H154 zenon_He0 zenon_H115 zenon_Hb6 zenon_H9c zenon_Hb3 zenon_Hbb zenon_H2b9 zenon_H244 zenon_H26e zenon_H145 zenon_H13d zenon_H186 zenon_H142 zenon_H177 zenon_H17e zenon_H18a zenon_H14b zenon_H1a2 zenon_H1a3 zenon_H124 zenon_Hd5 zenon_H182 zenon_H100 zenon_H191 zenon_H6b zenon_H71 zenon_H1de zenon_H1ef zenon_H13b. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.25/10.42 apply (zenon_L1_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.25/10.42 apply (zenon_L2_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.25/10.42 apply (zenon_L3_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.25/10.42 apply (zenon_L4_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.25/10.42 apply (zenon_L5_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.25/10.42 apply (zenon_L6_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.25/10.42 apply (zenon_L8_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.25/10.42 apply (zenon_L9_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.25/10.42 apply (zenon_L10_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.25/10.42 apply (zenon_L12_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.25/10.42 apply (zenon_L13_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.25/10.42 apply (zenon_L14_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.25/10.42 apply (zenon_L15_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.25/10.42 apply (zenon_L17_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.25/10.42 apply (zenon_L18_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.25/10.42 apply (zenon_L19_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.25/10.42 apply (zenon_L20_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.25/10.42 apply (zenon_L21_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.25/10.42 apply (zenon_L22_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.25/10.42 apply (zenon_L113_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.25/10.42 apply (zenon_L24_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.25/10.42 apply (zenon_L25_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.25/10.42 apply (zenon_L26_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.25/10.42 apply (zenon_L27_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.25/10.42 apply (zenon_L30_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.25/10.42 apply (zenon_L31_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.25/10.42 apply (zenon_L32_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H8b. zenon_intro zenon_H190. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H190). zenon_intro zenon_H8c. zenon_intro zenon_H1c8. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.42 apply (zenon_L29_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.42 apply (zenon_L42_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.42 apply (zenon_L335_); trivial. % 10.25/10.42 apply (zenon_L53_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.25/10.42 apply (zenon_L145_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.25/10.42 apply (zenon_L56_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hef. zenon_intro zenon_H170. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_Ha3. zenon_intro zenon_H1d3. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.42 apply (zenon_L29_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.42 apply (zenon_L204_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.25/10.42 apply (zenon_L33_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.25/10.42 exact (zenon_H6b zenon_H6f). % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.25/10.42 apply (zenon_L339_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.25/10.42 apply (zenon_L65_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.25/10.42 apply (zenon_L340_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.25/10.42 apply (zenon_L72_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.25/10.42 exact (zenon_Ha3 zenon_Ha2). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.42 apply (zenon_L74_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.42 apply (zenon_L340_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.42 apply (zenon_L62_); trivial. % 10.25/10.42 apply (zenon_L64_); trivial. % 10.25/10.42 apply (zenon_L187_); trivial. % 10.25/10.42 apply (zenon_L71_); trivial. % 10.25/10.42 apply (zenon_L343_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.25/10.42 apply (zenon_L339_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.25/10.42 apply (zenon_L205_); trivial. % 10.25/10.42 apply (zenon_L191_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.25/10.42 apply (zenon_L147_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.25/10.42 apply (zenon_L148_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.25/10.42 apply (zenon_L149_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.25/10.42 apply (zenon_L150_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.25/10.42 apply (zenon_L151_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H163. zenon_intro zenon_H2e. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.42 apply (zenon_L29_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.42 apply (zenon_L281_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.42 apply (zenon_L295_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.25/10.42 apply (zenon_L33_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.25/10.42 exact (zenon_H6b zenon_H6f). % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.42 exact (zenon_H30 zenon_H2d). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.42 exact (zenon_H6b zenon_H6f). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.42 apply (zenon_L45_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.42 apply (zenon_L283_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.25/10.42 apply (zenon_L44_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.25/10.42 apply (zenon_L45_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.25/10.42 exact (zenon_H71 zenon_H74). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.42 apply (zenon_L121_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.42 apply (zenon_L193_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.42 exact (zenon_H163 zenon_H103). % 10.25/10.42 apply (zenon_L218_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.42 apply (zenon_L35_); trivial. % 10.25/10.42 apply (zenon_L344_); trivial. % 10.25/10.42 apply (zenon_L47_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.42 apply (zenon_L91_); trivial. % 10.25/10.42 apply (zenon_L345_); trivial. % 10.25/10.42 apply (zenon_L347_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.25/10.42 apply (zenon_L154_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.25/10.42 apply (zenon_L155_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_Hc3. zenon_intro zenon_H1bf. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H163. zenon_intro zenon_H83. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.25/10.42 apply (zenon_L459_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.25/10.42 apply (zenon_L157_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.25/10.42 apply (zenon_L158_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.25/10.42 apply (zenon_L159_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.25/10.42 apply (zenon_L160_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.25/10.42 apply (zenon_L161_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_Hd4. zenon_intro zenon_H1d0. % 10.25/10.42 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_Hff. zenon_intro zenon_Hf2. % 10.25/10.42 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.42 apply (zenon_L29_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.42 apply (zenon_L29_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.25/10.42 apply (zenon_L33_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.25/10.42 exact (zenon_H6b zenon_H6f). % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.25/10.42 apply (zenon_L460_); trivial. % 10.25/10.42 apply (zenon_L40_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.42 apply (zenon_L454_); trivial. % 10.25/10.42 apply (zenon_L255_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.42 apply (zenon_L54_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.42 apply (zenon_L134_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.42 exact (zenon_H6b zenon_H6f). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.42 apply (zenon_L462_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.42 apply (zenon_L463_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.42 apply (zenon_L292_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.42 apply (zenon_L461_); trivial. % 10.25/10.42 exact (zenon_Hf3 zenon_Hef). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.42 apply (zenon_L91_); trivial. % 10.25/10.42 apply (zenon_L464_); trivial. % 10.25/10.42 apply (zenon_L240_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.25/10.42 apply (zenon_L164_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.25/10.42 apply (zenon_L165_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.25/10.42 apply (zenon_L166_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.25/10.42 apply (zenon_L167_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.25/10.42 apply (zenon_L242_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.25/10.42 apply (zenon_L169_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.25/10.42 apply (zenon_L171_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.25/10.42 apply (zenon_L172_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.25/10.42 apply (zenon_L173_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.25/10.42 apply (zenon_L174_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.25/10.42 apply (zenon_L276_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.25/10.42 apply (zenon_L177_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.25/10.42 apply (zenon_L178_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.25/10.42 apply (zenon_L179_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.25/10.42 apply (zenon_L180_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.25/10.42 apply (zenon_L181_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.25/10.42 apply (zenon_L182_); trivial. % 10.25/10.42 apply (zenon_L183_); trivial. % 10.25/10.42 (* end of lemma zenon_L465_ *) % 10.25/10.42 assert (zenon_L466_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.42 do 0 intro. intros zenon_H2b9 zenon_Hf4 zenon_Hf6 zenon_H177 zenon_Hba zenon_Hc4 zenon_H85 zenon_Hfd zenon_H127. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.42 apply (zenon_L89_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.42 apply (zenon_L197_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.42 apply (zenon_L45_); trivial. % 10.25/10.42 apply (zenon_L199_); trivial. % 10.25/10.42 (* end of lemma zenon_L466_ *) % 10.25/10.42 assert (zenon_L467_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> False). % 10.25/10.42 do 0 intro. intros zenon_H2e0 zenon_H30 zenon_H101 zenon_H100 zenon_H31 zenon_H287 zenon_H51 zenon_Hc0 zenon_H1b2 zenon_Hc4 zenon_H28c zenon_H9a zenon_H91. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e1 ]. % 10.25/10.42 exact (zenon_H30 zenon_H2d). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H2e2 ]. % 10.25/10.42 apply (zenon_L61_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H119 ]. % 10.25/10.42 apply (zenon_L302_); trivial. % 10.25/10.42 apply (zenon_L69_); trivial. % 10.25/10.42 (* end of lemma zenon_L467_ *) % 10.25/10.42 assert (zenon_L468_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.42 do 0 intro. intros zenon_He0 zenon_H13d zenon_Hbb zenon_Hef zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H135 zenon_H130 zenon_H145 zenon_H91 zenon_H9a zenon_H28c zenon_Hc4 zenon_H1b2 zenon_Hc0 zenon_H287 zenon_H31 zenon_H100 zenon_H101 zenon_H30 zenon_H2e0 zenon_H272 zenon_He9 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_H158 zenon_H104 zenon_H298 zenon_H85 zenon_H76. % 10.25/10.42 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.42 apply (zenon_L87_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.42 apply (zenon_L193_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.42 apply (zenon_L467_); trivial. % 10.25/10.42 apply (zenon_L326_); trivial. % 10.25/10.42 (* end of lemma zenon_L468_ *) % 10.25/10.42 assert (zenon_L469_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.25/10.42 do 0 intro. intros zenon_H124 zenon_H2e0 zenon_H30 zenon_H100 zenon_H31 zenon_H287 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_H9a zenon_H91 zenon_H145 zenon_H130 zenon_H135 zenon_H142 zenon_H1f zenon_H94 zenon_H138 zenon_Hbb zenon_H13d zenon_H76 zenon_H85 zenon_H298 zenon_H104 zenon_H158 zenon_H99 zenon_Hf4 zenon_H1e5 zenon_He9 zenon_H272 zenon_Hc4 zenon_H15b zenon_Hfd zenon_H154 zenon_H127 zenon_H157 zenon_He0 zenon_Hc6 zenon_Hef. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.42 apply (zenon_L121_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.42 apply (zenon_L468_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.42 apply (zenon_L329_); trivial. % 10.25/10.42 apply (zenon_L75_); trivial. % 10.25/10.42 (* end of lemma zenon_L469_ *) % 10.25/10.42 assert (zenon_L470_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.25/10.42 do 0 intro. intros zenon_Hdf zenon_H177 zenon_Hf6 zenon_H2b9 zenon_Hc6 zenon_He0 zenon_H157 zenon_H127 zenon_H154 zenon_Hfd zenon_H15b zenon_Hc4 zenon_H272 zenon_He9 zenon_H1e5 zenon_H99 zenon_H158 zenon_H104 zenon_H298 zenon_H85 zenon_H76 zenon_H13d zenon_Hbb zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H135 zenon_H130 zenon_H145 zenon_H9a zenon_H28c zenon_H1b2 zenon_Hc0 zenon_H287 zenon_H31 zenon_H100 zenon_H30 zenon_H2e0 zenon_H124 zenon_Hcd zenon_Hda zenon_Hef zenon_Hf4. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.42 apply (zenon_L466_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.42 apply (zenon_L469_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.42 apply (zenon_L50_); trivial. % 10.25/10.42 apply (zenon_L97_); trivial. % 10.25/10.42 (* end of lemma zenon_L470_ *) % 10.25/10.42 assert (zenon_L471_ : ((op (e1) (e0)) = (e3)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((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 (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.42 do 0 intro. intros zenon_H13c zenon_H24e zenon_H115 zenon_H2e0 zenon_H100 zenon_H99 zenon_H18a zenon_H31 zenon_H130 zenon_H104 zenon_H186 zenon_H1e5 zenon_Hfd zenon_H177 zenon_H298 zenon_H158 zenon_H272 zenon_He0 zenon_H1de zenon_H1e1 zenon_Hb6 zenon_H12d zenon_H30 zenon_H6b zenon_Hdf zenon_H145 zenon_H135 zenon_H17e zenon_H13d zenon_H2b9 zenon_H27c zenon_H2bc zenon_H15b zenon_H154 zenon_H157 zenon_H262 zenon_H293 zenon_H2ab zenon_H1ef zenon_H1cb zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_H289 zenon_H171 zenon_H124 zenon_H142 zenon_H94 zenon_H138 zenon_Hbb zenon_H2ae zenon_H76 zenon_H290 zenon_H278 zenon_H245 zenon_H14b zenon_H15e zenon_Hc6 zenon_H71 zenon_H1f zenon_Hca zenon_H287 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_Hf4 zenon_Hcd zenon_Hda zenon_H85 zenon_He9 zenon_H127. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.25/10.42 apply (zenon_L33_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.25/10.42 exact (zenon_H6b zenon_H6f). % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.42 exact (zenon_H30 zenon_H2d). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.42 exact (zenon_H6b zenon_H6f). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.42 apply (zenon_L248_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.42 apply (zenon_L330_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.42 apply (zenon_L310_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.42 apply (zenon_L45_); trivial. % 10.25/10.42 apply (zenon_L199_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.42 apply (zenon_L35_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.25/10.42 apply (zenon_L470_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.25/10.42 apply (zenon_L65_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.42 apply (zenon_L327_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.42 apply (zenon_L197_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.42 apply (zenon_L45_); trivial. % 10.25/10.42 apply (zenon_L199_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.42 apply (zenon_L469_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.42 apply (zenon_L50_); trivial. % 10.25/10.42 apply (zenon_L97_); trivial. % 10.25/10.42 apply (zenon_L187_); trivial. % 10.25/10.42 apply (zenon_L77_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.42 exact (zenon_H30 zenon_H2d). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.42 exact (zenon_H6b zenon_H6f). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.42 apply (zenon_L115_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.42 apply (zenon_L331_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.42 apply (zenon_L197_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.42 apply (zenon_L45_); trivial. % 10.25/10.42 apply (zenon_L199_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.42 apply (zenon_L310_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.42 apply (zenon_L50_); trivial. % 10.25/10.42 apply (zenon_L51_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.42 apply (zenon_L296_); trivial. % 10.25/10.42 apply (zenon_L71_); trivial. % 10.25/10.42 apply (zenon_L77_); trivial. % 10.25/10.42 (* end of lemma zenon_L471_ *) % 10.25/10.42 assert (zenon_L472_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.42 do 0 intro. intros zenon_H2b9 zenon_H31 zenon_H152 zenon_H36 zenon_Hf4 zenon_Hc4 zenon_H85 zenon_Hfd zenon_H127. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.42 apply (zenon_L301_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.42 apply (zenon_L310_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.42 apply (zenon_L45_); trivial. % 10.25/10.42 apply (zenon_L199_); trivial. % 10.25/10.42 (* end of lemma zenon_L472_ *) % 10.25/10.42 assert (zenon_L473_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.42 do 0 intro. intros zenon_H12d zenon_H30 zenon_H6b zenon_Ha5 zenon_H99 zenon_H1e1 zenon_H18a zenon_H130 zenon_H104 zenon_H186 zenon_H2b9 zenon_H31 zenon_H152 zenon_Hf4 zenon_H85 zenon_Hfd zenon_H94 zenon_H2ab zenon_He9 zenon_H127. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.42 exact (zenon_H30 zenon_H2d). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.42 exact (zenon_H6b zenon_H6f). % 10.25/10.42 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.42 apply (zenon_L243_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.42 apply (zenon_L472_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.42 apply (zenon_L297_); trivial. % 10.25/10.42 apply (zenon_L71_); trivial. % 10.25/10.42 apply (zenon_L77_); trivial. % 10.25/10.42 (* end of lemma zenon_L473_ *) % 10.25/10.42 assert (zenon_L474_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.42 do 0 intro. intros zenon_Hb6 zenon_H24e zenon_Hda zenon_Hcd zenon_H124 zenon_H15b zenon_H154 zenon_H157 zenon_Hc6 zenon_H177 zenon_Hdf zenon_H115 zenon_He0 zenon_H13d zenon_Hbb zenon_H138 zenon_H1f zenon_H142 zenon_H135 zenon_H145 zenon_H28c zenon_H1b2 zenon_Hc0 zenon_H287 zenon_H100 zenon_H2e0 zenon_H272 zenon_H1e5 zenon_H158 zenon_H298 zenon_H76 zenon_H12d zenon_H30 zenon_H6b zenon_H99 zenon_H1e1 zenon_H18a zenon_H130 zenon_H104 zenon_H186 zenon_H2b9 zenon_H31 zenon_H152 zenon_Hf4 zenon_H85 zenon_Hfd zenon_H94 zenon_H2ab zenon_He9 zenon_H127. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.25/10.42 apply (zenon_L33_); trivial. % 10.25/10.42 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.25/10.43 exact (zenon_H6b zenon_H6f). % 10.25/10.43 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.43 exact (zenon_H30 zenon_H2d). % 10.25/10.43 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.43 exact (zenon_H6b zenon_H6f). % 10.25/10.43 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.43 apply (zenon_L243_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.43 apply (zenon_L472_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.43 apply (zenon_L297_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.25/10.43 apply (zenon_L470_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.25/10.43 apply (zenon_L65_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.43 apply (zenon_L301_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.43 apply (zenon_L468_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.43 apply (zenon_L45_); trivial. % 10.25/10.43 apply (zenon_L199_); trivial. % 10.25/10.43 apply (zenon_L187_); trivial. % 10.25/10.43 apply (zenon_L77_); trivial. % 10.25/10.43 apply (zenon_L473_); trivial. % 10.25/10.43 (* end of lemma zenon_L474_ *) % 10.25/10.43 assert (zenon_L475_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((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 (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.25/10.43 do 0 intro. intros zenon_He0 zenon_H1de zenon_H1e1 zenon_Hb6 zenon_H12d zenon_H30 zenon_H6b zenon_H99 zenon_H18a zenon_H130 zenon_H104 zenon_H186 zenon_H1e5 zenon_Hdf zenon_Hfd zenon_H145 zenon_H1f zenon_H135 zenon_H17e zenon_H13d zenon_Hda zenon_H2b9 zenon_H27c zenon_H2bc zenon_H15b zenon_H154 zenon_H262 zenon_H293 zenon_H2ab zenon_H1ef zenon_H1cb zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H202 zenon_H289 zenon_H171 zenon_H124 zenon_H142 zenon_H94 zenon_H138 zenon_Hbb zenon_H2ae zenon_H85 zenon_He9 zenon_H127 zenon_H76 zenon_H290 zenon_H278 zenon_H245 zenon_H14b zenon_H15e zenon_H101 zenon_Hf4 zenon_H31 zenon_Ha4 zenon_H287 zenon_Hc0 zenon_H1b2 zenon_Hc4 zenon_H28c zenon_He5 zenon_H157. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.43 apply (zenon_L323_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.43 apply (zenon_L193_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.43 apply (zenon_L302_); trivial. % 10.25/10.43 apply (zenon_L240_); trivial. % 10.25/10.43 (* end of lemma zenon_L475_ *) % 10.25/10.43 assert (zenon_L476_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.25/10.43 do 0 intro. intros zenon_He0 zenon_H127 zenon_He9 zenon_H2ab zenon_H13c zenon_Hfd zenon_Hf4 zenon_H124 zenon_H171 zenon_H293 zenon_H14b zenon_H177 zenon_H15e zenon_H186 zenon_H104 zenon_H18a zenon_H1e1 zenon_H150 zenon_H245 zenon_H28c zenon_H1b2 zenon_Hc0 zenon_H287 zenon_H278 zenon_H290 zenon_H76 zenon_H2b9 zenon_H9a zenon_H99 zenon_H145 zenon_H31 zenon_H130 zenon_H135 zenon_H142 zenon_H1f zenon_H94 zenon_H138 zenon_Hbb zenon_H13d zenon_H6b zenon_H30 zenon_H12d zenon_Hc4 zenon_H85 zenon_H182 zenon_Hdb zenon_He5 zenon_H157. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.43 apply (zenon_L362_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.43 apply (zenon_L45_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.43 apply (zenon_L307_); trivial. % 10.25/10.43 apply (zenon_L240_); trivial. % 10.25/10.43 (* end of lemma zenon_L476_ *) % 10.25/10.43 assert (zenon_L477_ : ((op (e2) (e1)) = (e2)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 10.25/10.43 do 0 intro. intros zenon_Hc3 zenon_H91 zenon_H171. % 10.25/10.43 elim (classic ((op (e2) (e1)) = (op (e2) (e1)))); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H1b4 ]. % 10.25/10.43 cut (((op (e2) (e1)) = (op (e2) (e1))) = ((op (e1) (e1)) = (op (e2) (e1)))). % 10.25/10.43 intro zenon_D_pnotp. % 10.25/10.43 apply zenon_H171. % 10.25/10.43 rewrite <- zenon_D_pnotp. % 10.25/10.43 exact zenon_H1b3. % 10.25/10.43 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 10.25/10.43 cut (((op (e2) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e3]. % 10.25/10.43 congruence. % 10.25/10.43 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e1) (e1)))). % 10.25/10.43 intro zenon_D_pnotp. % 10.25/10.43 apply zenon_H2e3. % 10.25/10.43 rewrite <- zenon_D_pnotp. % 10.25/10.43 exact zenon_Hc3. % 10.25/10.43 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 10.25/10.43 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 10.25/10.43 congruence. % 10.25/10.43 apply zenon_H1b4. apply refl_equal. % 10.25/10.43 apply zenon_H11e. apply sym_equal. exact zenon_H91. % 10.25/10.43 apply zenon_H1b4. apply refl_equal. % 10.25/10.43 apply zenon_H1b4. apply refl_equal. % 10.25/10.43 (* end of lemma zenon_L477_ *) % 10.25/10.43 assert (zenon_L478_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((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 (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e0) (e2)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.25/10.43 do 0 intro. intros zenon_He0 zenon_H127 zenon_He9 zenon_H2ab zenon_H13c zenon_Hfd zenon_H85 zenon_Hf4 zenon_H124 zenon_H293 zenon_H14b zenon_H177 zenon_H15e zenon_H186 zenon_H104 zenon_H18a zenon_H1e1 zenon_H150 zenon_H245 zenon_H278 zenon_H290 zenon_H76 zenon_H2b9 zenon_H99 zenon_H145 zenon_H130 zenon_H135 zenon_H142 zenon_H1f zenon_H94 zenon_H138 zenon_Hbb zenon_H13d zenon_H6b zenon_H12d zenon_H171 zenon_H91 zenon_H9a zenon_H28c zenon_Hc4 zenon_H1b2 zenon_Hc0 zenon_H287 zenon_H31 zenon_H100 zenon_H101 zenon_H30 zenon_H2e0 zenon_He5 zenon_H157. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.43 apply (zenon_L362_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.43 apply (zenon_L477_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.43 apply (zenon_L467_); trivial. % 10.25/10.43 apply (zenon_L240_); trivial. % 10.25/10.43 (* end of lemma zenon_L478_ *) % 10.25/10.43 assert (zenon_L479_ : (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e1)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.25/10.43 do 0 intro. intros zenon_H157 zenon_He5 zenon_H2e0 zenon_H30 zenon_H100 zenon_H31 zenon_H287 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_H9a zenon_H91 zenon_H171 zenon_H12d zenon_H6b zenon_H13d zenon_Hbb zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H135 zenon_H130 zenon_H145 zenon_H99 zenon_H2b9 zenon_H76 zenon_H290 zenon_H278 zenon_H245 zenon_H1e1 zenon_H18a zenon_H104 zenon_H186 zenon_H15e zenon_H177 zenon_H14b zenon_H293 zenon_H124 zenon_Hf4 zenon_H85 zenon_Hfd zenon_H13c zenon_H2ab zenon_He9 zenon_H127 zenon_He0 zenon_Hc4 zenon_H150 zenon_Hc6 zenon_Hef. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.43 apply (zenon_L121_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.43 apply (zenon_L478_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.43 apply (zenon_L102_); trivial. % 10.25/10.43 apply (zenon_L75_); trivial. % 10.25/10.43 (* end of lemma zenon_L479_ *) % 10.25/10.43 assert (zenon_L480_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.25/10.43 do 0 intro. intros zenon_H17e zenon_H157 zenon_He5 zenon_Hdb zenon_H182 zenon_H85 zenon_Hc4 zenon_H12d zenon_H30 zenon_H6b zenon_H13d zenon_Hbb zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H135 zenon_H130 zenon_H31 zenon_H145 zenon_H99 zenon_H9a zenon_H2b9 zenon_H76 zenon_H290 zenon_H278 zenon_H287 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_H245 zenon_H1e1 zenon_H18a zenon_H186 zenon_H15e zenon_H177 zenon_H14b zenon_H293 zenon_H171 zenon_H124 zenon_Hf4 zenon_H2ab zenon_He9 zenon_H127 zenon_He0 zenon_Hfd zenon_H91 zenon_H150 zenon_Hda zenon_Hef zenon_H104. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.43 apply (zenon_L476_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.43 apply (zenon_L237_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.43 apply (zenon_L308_); trivial. % 10.25/10.43 apply (zenon_L341_); trivial. % 10.25/10.43 (* end of lemma zenon_L480_ *) % 10.25/10.43 assert (zenon_L481_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 10.25/10.43 do 0 intro. intros zenon_Hdf zenon_H2e0 zenon_H100 zenon_Hc6 zenon_H127 zenon_Hfd zenon_H85 zenon_Hc4 zenon_H17e zenon_H157 zenon_H182 zenon_H12d zenon_H30 zenon_H6b zenon_H13d zenon_Hbb zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H135 zenon_H130 zenon_H31 zenon_H145 zenon_H99 zenon_H9a zenon_H2b9 zenon_H76 zenon_H290 zenon_H278 zenon_H287 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_H245 zenon_H1e1 zenon_H18a zenon_H186 zenon_H15e zenon_H177 zenon_H14b zenon_H293 zenon_H171 zenon_H124 zenon_Hf4 zenon_H2ab zenon_He9 zenon_He0 zenon_H150 zenon_Hda zenon_Hef zenon_H104 zenon_Hf6 zenon_H24b zenon_He5. % 10.25/10.43 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.43 apply (zenon_L466_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.43 apply (zenon_L479_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.43 apply (zenon_L237_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.43 apply (zenon_L308_); trivial. % 10.25/10.43 apply (zenon_L341_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.43 apply (zenon_L89_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.43 apply (zenon_L480_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.43 apply (zenon_L45_); trivial. % 10.25/10.43 apply (zenon_L199_); trivial. % 10.25/10.43 apply (zenon_L213_); trivial. % 10.25/10.43 (* end of lemma zenon_L481_ *) % 10.25/10.43 assert (zenon_L482_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (e0))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.25/10.43 do 0 intro. intros zenon_H17e zenon_H157 zenon_He5 zenon_H2e0 zenon_H30 zenon_H101 zenon_H100 zenon_H31 zenon_H287 zenon_Hc0 zenon_H1b2 zenon_Hc4 zenon_H28c zenon_H9a zenon_H171 zenon_H12d zenon_H6b zenon_H13d zenon_Hbb zenon_H138 zenon_H94 zenon_H1f zenon_H142 zenon_H135 zenon_H130 zenon_H145 zenon_H99 zenon_H2b9 zenon_H76 zenon_H290 zenon_H278 zenon_H245 zenon_H1e1 zenon_H18a zenon_H186 zenon_H15e zenon_H177 zenon_H14b zenon_H293 zenon_H124 zenon_Hf4 zenon_H85 zenon_H2ab zenon_He9 zenon_H127 zenon_He0 zenon_Hfd zenon_H91 zenon_H150 zenon_Hda zenon_Hef zenon_H104. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.43 apply (zenon_L478_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.43 apply (zenon_L237_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.43 apply (zenon_L308_); trivial. % 10.25/10.43 apply (zenon_L341_); trivial. % 10.25/10.43 (* end of lemma zenon_L482_ *) % 10.25/10.43 assert (zenon_L483_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((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 (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.25/10.43 do 0 intro. intros zenon_Hca zenon_H71 zenon_H1e5 zenon_H2ae zenon_H289 zenon_H202 zenon_H37 zenon_H47 zenon_H5b zenon_H18d zenon_H1cb zenon_H1ef zenon_H262 zenon_H154 zenon_H15b zenon_H2bc zenon_H27c zenon_H127 zenon_He9 zenon_H2ab zenon_H94 zenon_Hfd zenon_H85 zenon_Hf4 zenon_H31 zenon_H2b9 zenon_H186 zenon_H104 zenon_H130 zenon_H18a zenon_H99 zenon_H6b zenon_H30 zenon_H12d zenon_Hda zenon_H150 zenon_He0 zenon_H124 zenon_H293 zenon_H14b zenon_H177 zenon_H15e zenon_H245 zenon_H278 zenon_H290 zenon_H76 zenon_H145 zenon_H135 zenon_H142 zenon_H1f zenon_H138 zenon_Hbb zenon_H13d zenon_H171 zenon_H28c zenon_H1b2 zenon_Hc0 zenon_H287 zenon_H100 zenon_H2e0 zenon_He5 zenon_H157 zenon_H17e zenon_H115 zenon_Hdf zenon_Hc6 zenon_H182 zenon_H24b zenon_H24e zenon_Hb6 zenon_H1e1 zenon_H1de. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.25/10.43 apply (zenon_L355_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.25/10.43 apply (zenon_L33_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.25/10.43 exact (zenon_H6b zenon_H6f). % 10.25/10.43 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.43 exact (zenon_H30 zenon_H2d). % 10.25/10.43 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.43 exact (zenon_H6b zenon_H6f). % 10.25/10.43 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.43 apply (zenon_L248_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.43 apply (zenon_L121_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.43 apply (zenon_L475_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.43 apply (zenon_L102_); trivial. % 10.25/10.43 apply (zenon_L304_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.43 apply (zenon_L197_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.43 apply (zenon_L45_); trivial. % 10.25/10.43 apply (zenon_L199_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.43 apply (zenon_L310_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.43 apply (zenon_L476_); trivial. % 10.25/10.43 apply (zenon_L213_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.43 apply (zenon_L35_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.25/10.43 apply (zenon_L481_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.25/10.43 apply (zenon_L65_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.43 apply (zenon_L475_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.43 apply (zenon_L479_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.43 apply (zenon_L45_); trivial. % 10.25/10.43 apply (zenon_L199_); trivial. % 10.25/10.43 apply (zenon_L187_); trivial. % 10.25/10.43 apply (zenon_L77_); trivial. % 10.25/10.43 apply (zenon_L314_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.25/10.43 apply (zenon_L33_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.25/10.43 exact (zenon_H6b zenon_H6f). % 10.25/10.43 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.43 exact (zenon_H30 zenon_H2d). % 10.25/10.43 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.43 exact (zenon_H6b zenon_H6f). % 10.25/10.43 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.43 apply (zenon_L115_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.43 apply (zenon_L472_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.43 apply (zenon_L35_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.25/10.43 apply (zenon_L481_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.25/10.43 apply (zenon_L65_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.43 apply (zenon_L301_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.43 apply (zenon_L482_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.43 apply (zenon_L45_); trivial. % 10.25/10.43 apply (zenon_L199_); trivial. % 10.25/10.43 apply (zenon_L187_); trivial. % 10.25/10.43 apply (zenon_L77_); trivial. % 10.25/10.43 apply (zenon_L473_); trivial. % 10.25/10.43 apply (zenon_L171_); trivial. % 10.25/10.43 (* end of lemma zenon_L483_ *) % 10.25/10.43 assert (zenon_L484_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.25/10.43 do 0 intro. intros zenon_H1e6 zenon_H51 zenon_Hf4. % 10.25/10.43 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H127. zenon_intro zenon_H1e7. % 10.25/10.43 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1e5. zenon_intro zenon_H80. % 10.25/10.43 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.25/10.43 apply (zenon_L328_); trivial. % 10.25/10.43 (* end of lemma zenon_L484_ *) % 10.25/10.43 assert (zenon_L485_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e2) (e1)) = (e2))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.43 do 0 intro. intros zenon_He0 zenon_Hbb zenon_Hba zenon_H1bd zenon_H1e6 zenon_H272 zenon_He9 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_H158 zenon_H104 zenon_H298 zenon_H85 zenon_H76. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.43 apply (zenon_L43_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.43 exact (zenon_H1bd zenon_Hc3). % 10.25/10.43 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.43 apply (zenon_L484_); trivial. % 10.25/10.43 apply (zenon_L326_); trivial. % 10.25/10.43 (* end of lemma zenon_L485_ *) % 10.25/10.43 assert (zenon_L486_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.25/10.43 do 0 intro. intros zenon_H2d zenon_Ha4 zenon_H85. % 10.25/10.43 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.25/10.43 cut (((e2) = (e2)) = ((e0) = (e2))). % 10.25/10.43 intro zenon_D_pnotp. % 10.25/10.43 apply zenon_H85. % 10.25/10.43 rewrite <- zenon_D_pnotp. % 10.25/10.43 exact zenon_H86. % 10.25/10.43 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.25/10.43 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 10.25/10.43 congruence. % 10.25/10.43 cut (((op (e0) (e1)) = (e0)) = ((e2) = (e0))). % 10.25/10.43 intro zenon_D_pnotp. % 10.25/10.43 apply zenon_H88. % 10.25/10.43 rewrite <- zenon_D_pnotp. % 10.25/10.43 exact zenon_H2d. % 10.25/10.43 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.43 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 10.25/10.43 congruence. % 10.25/10.43 exact (zenon_H14a zenon_Ha4). % 10.25/10.43 apply zenon_H84. apply refl_equal. % 10.25/10.43 apply zenon_H87. apply refl_equal. % 10.25/10.43 apply zenon_H87. apply refl_equal. % 10.25/10.43 (* end of lemma zenon_L486_ *) % 10.25/10.43 assert (zenon_L487_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> (~((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.43 do 0 intro. intros zenon_He0 zenon_H12d zenon_H37 zenon_H1f zenon_H6b zenon_H14b zenon_H15e zenon_H15b zenon_Hfd zenon_H154 zenon_H157 zenon_H1a2 zenon_H1e6 zenon_H1bd zenon_Hce zenon_Hcd zenon_H272 zenon_He9 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_H158 zenon_H104 zenon_H298 zenon_H85 zenon_H76. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.43 apply (zenon_L368_); trivial. % 10.25/10.43 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.43 exact (zenon_H1bd zenon_Hc3). % 10.25/10.43 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.43 apply (zenon_L48_); trivial. % 10.25/10.43 apply (zenon_L326_); trivial. % 10.25/10.43 (* end of lemma zenon_L487_ *) % 10.25/10.43 assert (zenon_L488_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.25/10.43 do 0 intro. intros zenon_H15e zenon_H14b zenon_H127 zenon_He9 zenon_H103 zenon_H6b zenon_H1f zenon_H37 zenon_H12d zenon_He5 zenon_Hfd. % 10.25/10.43 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.44 apply (zenon_L54_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.44 apply (zenon_L90_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.44 apply (zenon_L364_); trivial. % 10.25/10.44 apply (zenon_L103_); trivial. % 10.25/10.44 (* end of lemma zenon_L488_ *) % 10.25/10.44 assert (zenon_L489_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H15e zenon_He9 zenon_H85 zenon_H94 zenon_H1f zenon_Hb6 zenon_Hcd zenon_H17e zenon_H104 zenon_H6a zenon_Hfd zenon_H91 zenon_H186 zenon_H1ed zenon_H24b. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.44 apply (zenon_L54_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.44 apply (zenon_L251_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.44 apply (zenon_L91_); trivial. % 10.25/10.44 apply (zenon_L254_); trivial. % 10.25/10.44 (* end of lemma zenon_L489_ *) % 10.25/10.44 assert (zenon_L490_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e2)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H29b zenon_H202 zenon_H18a zenon_H278 zenon_H13d zenon_H1a3 zenon_H157 zenon_Hda zenon_Hc6 zenon_Hdf zenon_H124 zenon_Hd5 zenon_Hbb zenon_H138 zenon_H18d zenon_H5b zenon_H47 zenon_H37 zenon_H135 zenon_H171 zenon_Hca zenon_H284 zenon_H28c zenon_H1ef zenon_H1de zenon_H1cb zenon_H289 zenon_H287 zenon_H290 zenon_H28f zenon_H293 zenon_H269 zenon_He6 zenon_H298 zenon_H15b zenon_Hc0 zenon_H281 zenon_H1b2 zenon_H29c zenon_H6b zenon_H27c zenon_H186 zenon_Hcd zenon_Hb6 zenon_H94 zenon_H15e zenon_H245 zenon_H1f zenon_H130 zenon_H2c5 zenon_Hfd zenon_Hf4 zenon_H85 zenon_H1ee zenon_H2ab zenon_H24b zenon_H91 zenon_H104 zenon_H17e zenon_H1f3 zenon_H90 zenon_H99 zenon_H272 zenon_H1ed zenon_He9 zenon_H76. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.44 apply (zenon_L54_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.44 apply (zenon_L371_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.44 apply (zenon_L252_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.25/10.44 apply (zenon_L489_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.25/10.44 apply (zenon_L310_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.25/10.44 exact (zenon_H90 zenon_H8b). % 10.25/10.44 apply (zenon_L377_); trivial. % 10.25/10.44 (* end of lemma zenon_L490_ *) % 10.25/10.44 assert (zenon_L491_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> (~((op (e2) (e2)) = (e1))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H3c zenon_H163. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H2d. zenon_intro zenon_H3d. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H2f. zenon_intro zenon_H80. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.25/10.44 exact (zenon_H163 zenon_H103). % 10.25/10.44 (* end of lemma zenon_L491_ *) % 10.25/10.44 assert (zenon_L492_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H3e zenon_H1e5. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H2d. zenon_intro zenon_H3f. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H2f. zenon_intro zenon_H83. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.25/10.44 exact (zenon_H1e5 zenon_H189). % 10.25/10.44 (* end of lemma zenon_L492_ *) % 10.25/10.44 assert (zenon_L493_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H4b zenon_Hf4 zenon_H36. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H42. zenon_intro zenon_H4c. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H44. zenon_intro zenon_H8f. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.25/10.44 apply (zenon_L310_); trivial. % 10.25/10.44 (* end of lemma zenon_L493_ *) % 10.25/10.44 assert (zenon_L494_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H42 zenon_H2d zenon_H2e4. % 10.25/10.44 elim (classic ((op (e0) (e2)) = (op (e0) (e2)))); [ zenon_intro zenon_H48 | zenon_intro zenon_H49 ]. % 10.25/10.44 cut (((op (e0) (e2)) = (op (e0) (e2))) = ((op (e0) (e1)) = (op (e0) (e2)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2e4. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H48. % 10.25/10.44 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 10.25/10.44 cut (((op (e0) (e2)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e5]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e1)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2e5. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H42. % 10.25/10.44 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 10.25/10.44 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 10.25/10.44 congruence. % 10.25/10.44 apply zenon_H49. apply refl_equal. % 10.25/10.44 apply zenon_H2e6. apply sym_equal. exact zenon_H2d. % 10.25/10.44 apply zenon_H49. apply refl_equal. % 10.25/10.44 apply zenon_H49. apply refl_equal. % 10.25/10.44 (* end of lemma zenon_L494_ *) % 10.25/10.44 assert (zenon_L495_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H52 zenon_H2d zenon_H2e4. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H42. zenon_intro zenon_H53. % 10.25/10.44 apply (zenon_L494_); trivial. % 10.25/10.44 (* end of lemma zenon_L495_ *) % 10.25/10.44 assert (zenon_L496_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H56 zenon_H2d zenon_H2e7. % 10.25/10.44 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 10.25/10.44 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e1)) = (op (e0) (e3)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2e7. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H5c. % 10.25/10.44 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.25/10.44 cut (((op (e0) (e3)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e8]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e1)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2e8. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H56. % 10.25/10.44 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 10.25/10.44 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.25/10.44 congruence. % 10.25/10.44 apply zenon_H5d. apply refl_equal. % 10.25/10.44 apply zenon_H2e6. apply sym_equal. exact zenon_H2d. % 10.25/10.44 apply zenon_H5d. apply refl_equal. % 10.25/10.44 apply zenon_H5d. apply refl_equal. % 10.25/10.44 (* end of lemma zenon_L496_ *) % 10.25/10.44 assert (zenon_L497_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H5f zenon_H2d zenon_H2e7. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H56. zenon_intro zenon_H60. % 10.25/10.44 apply (zenon_L496_); trivial. % 10.25/10.44 (* end of lemma zenon_L497_ *) % 10.25/10.44 assert (zenon_L498_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H61 zenon_H2d zenon_H2e7. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H56. zenon_intro zenon_H62. % 10.25/10.44 apply (zenon_L496_); trivial. % 10.25/10.44 (* end of lemma zenon_L498_ *) % 10.25/10.44 assert (zenon_L499_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H70 zenon_H177 zenon_H36. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H6a. zenon_intro zenon_H72. % 10.25/10.44 apply (zenon_L282_); trivial. % 10.25/10.44 (* end of lemma zenon_L499_ *) % 10.25/10.44 assert (zenon_L500_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H75 zenon_H177 zenon_H36. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H6a. zenon_intro zenon_H77. % 10.25/10.44 apply (zenon_L282_); trivial. % 10.25/10.44 (* end of lemma zenon_L500_ *) % 10.25/10.44 assert (zenon_L501_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H89 zenon_H36 zenon_H9c. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 10.25/10.44 apply (zenon_L36_); trivial. % 10.25/10.44 (* end of lemma zenon_L501_ *) % 10.25/10.44 assert (zenon_L502_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H18f zenon_H36 zenon_H9c. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H8b. zenon_intro zenon_H190. % 10.25/10.44 apply (zenon_L36_); trivial. % 10.25/10.44 (* end of lemma zenon_L502_ *) % 10.25/10.44 assert (zenon_L503_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_Hed zenon_H36 zenon_H115. % 10.25/10.44 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hef. zenon_intro zenon_Hee. % 10.25/10.44 apply (zenon_L65_); trivial. % 10.25/10.44 (* end of lemma zenon_L503_ *) % 10.25/10.44 assert (zenon_L504_ : ((op (e1) (e1)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H6f zenon_H2d zenon_H173. % 10.25/10.44 elim (classic ((op (e1) (e1)) = (op (e1) (e1)))); [ zenon_intro zenon_H178 | zenon_intro zenon_H172 ]. % 10.25/10.44 cut (((op (e1) (e1)) = (op (e1) (e1))) = ((op (e0) (e1)) = (op (e1) (e1)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H173. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H178. % 10.25/10.44 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 10.25/10.44 cut (((op (e1) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e9]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e0) (e1)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2e9. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H6f. % 10.25/10.44 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 10.25/10.44 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 10.25/10.44 congruence. % 10.25/10.44 apply zenon_H172. apply refl_equal. % 10.25/10.44 apply zenon_H2e6. apply sym_equal. exact zenon_H2d. % 10.25/10.44 apply zenon_H172. apply refl_equal. % 10.25/10.44 apply zenon_H172. apply refl_equal. % 10.25/10.44 (* end of lemma zenon_L504_ *) % 10.25/10.44 assert (zenon_L505_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1ac zenon_H2d zenon_H173. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_Hb9. zenon_intro zenon_H1ad. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H71. zenon_intro zenon_H24. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.25/10.44 apply (zenon_L504_); trivial. % 10.25/10.44 (* end of lemma zenon_L505_ *) % 10.25/10.44 assert (zenon_L506_ : ((op (e3) (e3)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H79 zenon_Hc7 zenon_Hd5. % 10.25/10.44 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_Hd5. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_Hd6. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_Hd8. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H79. % 10.25/10.44 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.25/10.44 congruence. % 10.25/10.44 apply zenon_Hd7. apply refl_equal. % 10.25/10.44 apply zenon_Hc8. apply sym_equal. exact zenon_Hc7. % 10.25/10.44 apply zenon_Hd7. apply refl_equal. % 10.25/10.44 apply zenon_Hd7. apply refl_equal. % 10.25/10.44 (* end of lemma zenon_L506_ *) % 10.25/10.44 assert (zenon_L507_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_Hca zenon_Hb9 zenon_H85 zenon_H2d zenon_H100 zenon_H71 zenon_H79 zenon_Hd5. % 10.25/10.44 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.25/10.44 apply (zenon_L417_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.25/10.44 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e2) (e1)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H100. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H2d. % 10.25/10.44 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H286]. % 10.25/10.44 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 10.25/10.44 congruence. % 10.25/10.44 apply zenon_H39. apply refl_equal. % 10.25/10.44 apply zenon_H286. apply sym_equal. exact zenon_Hc4. % 10.25/10.44 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.25/10.44 exact (zenon_H71 zenon_H74). % 10.25/10.44 apply (zenon_L506_); trivial. % 10.25/10.44 (* end of lemma zenon_L507_ *) % 10.25/10.44 assert (zenon_L508_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1b0 zenon_Hca zenon_H85 zenon_H2d zenon_H100 zenon_Hd5. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb9. zenon_intro zenon_H1b1. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H71. zenon_intro zenon_H2a. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.25/10.44 apply (zenon_L507_); trivial. % 10.25/10.44 (* end of lemma zenon_L508_ *) % 10.25/10.44 assert (zenon_L509_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e0) (e1)) = (e0)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1b7 zenon_H2d. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H163. zenon_intro zenon_H2e. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.25/10.44 exact (zenon_H30 zenon_H2d). % 10.25/10.44 (* end of lemma zenon_L509_ *) % 10.25/10.44 assert (zenon_L510_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1be zenon_H1e5. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_Hc3. zenon_intro zenon_H1bf. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H163. zenon_intro zenon_H83. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.25/10.44 exact (zenon_H1e5 zenon_H189). % 10.25/10.44 (* end of lemma zenon_L510_ *) % 10.25/10.44 assert (zenon_L511_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e2)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H94 zenon_H46 zenon_Hba. % 10.25/10.44 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H94. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H46. % 10.25/10.44 cut (((e2) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 10.25/10.44 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 10.25/10.44 congruence. % 10.25/10.44 apply zenon_H97. apply refl_equal. % 10.25/10.44 apply zenon_Hbf. apply sym_equal. exact zenon_Hba. % 10.25/10.44 (* end of lemma zenon_L511_ *) % 10.25/10.44 assert (zenon_L512_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> ((op (e2) (e1)) = (e2)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H3c zenon_Hc3. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H2d. zenon_intro zenon_H3d. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H2f. zenon_intro zenon_H80. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.25/10.44 exact (zenon_H1bd zenon_Hc3). % 10.25/10.44 (* end of lemma zenon_L512_ *) % 10.25/10.44 assert (zenon_L513_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H4b zenon_Hc3 zenon_H171. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H42. zenon_intro zenon_H4c. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H44. zenon_intro zenon_H8f. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.25/10.44 apply (zenon_L477_); trivial. % 10.25/10.44 (* end of lemma zenon_L513_ *) % 10.25/10.44 assert (zenon_L514_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1b0 zenon_Hc3 zenon_H1b2. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb9. zenon_intro zenon_H1b1. % 10.25/10.44 apply (zenon_L152_); trivial. % 10.25/10.44 (* end of lemma zenon_L514_ *) % 10.25/10.44 assert (zenon_L515_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_Hd4 zenon_Hc3 zenon_H2ea. % 10.25/10.44 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H1cc | zenon_intro zenon_H1cd ]. % 10.25/10.44 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e1)) = (op (e2) (e3)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2ea. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H1cc. % 10.25/10.44 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 10.25/10.44 cut (((op (e2) (e3)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2eb]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e2) (e1)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2eb. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_Hd4. % 10.25/10.44 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ec]. % 10.25/10.44 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1cd]. % 10.25/10.44 congruence. % 10.25/10.44 apply zenon_H1cd. apply refl_equal. % 10.25/10.44 apply zenon_H2ec. apply sym_equal. exact zenon_Hc3. % 10.25/10.44 apply zenon_H1cd. apply refl_equal. % 10.25/10.44 apply zenon_H1cd. apply refl_equal. % 10.25/10.44 (* end of lemma zenon_L515_ *) % 10.25/10.44 assert (zenon_L516_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1c9 zenon_Hc3 zenon_H2ea. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_Hd4. zenon_intro zenon_H1ca. % 10.25/10.44 apply (zenon_L515_); trivial. % 10.25/10.44 (* end of lemma zenon_L516_ *) % 10.25/10.44 assert (zenon_L517_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1cf zenon_Hc3 zenon_H2ea. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_Hd4. zenon_intro zenon_H1d0. % 10.25/10.44 apply (zenon_L515_); trivial. % 10.25/10.44 (* end of lemma zenon_L517_ *) % 10.25/10.44 assert (zenon_L518_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1d8 zenon_H36 zenon_H99. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1d8). zenon_intro zenon_H13b. zenon_intro zenon_H1d9. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1d9). zenon_intro zenon_H76. zenon_intro zenon_H24. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.25/10.44 apply (zenon_L312_); trivial. % 10.25/10.44 (* end of lemma zenon_L518_ *) % 10.25/10.44 assert (zenon_L519_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H12a zenon_He9 zenon_H2d zenon_H104 zenon_H36 zenon_Hfd zenon_Hc3 zenon_H13b zenon_H1de. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.25/10.44 apply (zenon_L134_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.25/10.44 apply (zenon_L225_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.25/10.44 apply (zenon_L73_); trivial. % 10.25/10.44 apply (zenon_L170_); trivial. % 10.25/10.44 (* end of lemma zenon_L519_ *) % 10.25/10.44 assert (zenon_L520_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e0) (e1)) = (e0)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1e1 zenon_H2d. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H127. zenon_intro zenon_H1e2. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H1e5. zenon_intro zenon_H2e. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.25/10.44 exact (zenon_H30 zenon_H2d). % 10.25/10.44 (* end of lemma zenon_L520_ *) % 10.25/10.44 assert (zenon_L521_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> ((op (e2) (e1)) = (e2)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1e6 zenon_Hc3. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H127. zenon_intro zenon_H1e7. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1e5. zenon_intro zenon_H80. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.25/10.44 exact (zenon_H1bd zenon_Hc3). % 10.25/10.44 (* end of lemma zenon_L521_ *) % 10.25/10.44 assert (zenon_L522_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H79 zenon_H131 zenon_H26e. % 10.25/10.44 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H26e. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_Hd6. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H26f. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H79. % 10.25/10.44 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.25/10.44 congruence. % 10.25/10.44 apply zenon_Hd7. apply refl_equal. % 10.25/10.44 apply zenon_H132. apply sym_equal. exact zenon_H131. % 10.25/10.44 apply zenon_Hd7. apply refl_equal. % 10.25/10.44 apply zenon_Hd7. apply refl_equal. % 10.25/10.44 (* end of lemma zenon_L522_ *) % 10.25/10.44 assert (zenon_L523_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1eb zenon_H67 zenon_H2cd. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ed. zenon_intro zenon_H1ec. % 10.25/10.44 apply (zenon_L387_); trivial. % 10.25/10.44 (* end of lemma zenon_L523_ *) % 10.25/10.44 assert (zenon_L524_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H2cf zenon_H26e zenon_H131 zenon_H1e5 zenon_H1ee zenon_H1eb zenon_H2cd. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2cf); [ zenon_intro zenon_H79 | zenon_intro zenon_H2d0 ]. % 10.25/10.44 apply (zenon_L522_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2d0); [ zenon_intro zenon_H189 | zenon_intro zenon_H2d1 ]. % 10.25/10.44 exact (zenon_H1e5 zenon_H189). % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H67 ]. % 10.25/10.44 exact (zenon_H1ee zenon_Hd3). % 10.25/10.44 apply (zenon_L523_); trivial. % 10.25/10.44 (* end of lemma zenon_L524_ *) % 10.25/10.44 assert (zenon_L525_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H79 zenon_H128 zenon_H2ed. % 10.25/10.44 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2ed. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_Hd6. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ee]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2ee. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H79. % 10.25/10.44 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26d]. % 10.25/10.44 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.25/10.44 congruence. % 10.25/10.44 apply zenon_Hd7. apply refl_equal. % 10.25/10.44 apply zenon_H26d. apply sym_equal. exact zenon_H128. % 10.25/10.44 apply zenon_Hd7. apply refl_equal. % 10.25/10.44 apply zenon_Hd7. apply refl_equal. % 10.25/10.44 (* end of lemma zenon_L525_ *) % 10.25/10.44 assert (zenon_L526_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H2cf zenon_H2ed zenon_H128 zenon_H1e5 zenon_H1ee zenon_H1eb zenon_H2cd. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2cf); [ zenon_intro zenon_H79 | zenon_intro zenon_H2d0 ]. % 10.25/10.44 apply (zenon_L525_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2d0); [ zenon_intro zenon_H189 | zenon_intro zenon_H2d1 ]. % 10.25/10.44 exact (zenon_H1e5 zenon_H189). % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H67 ]. % 10.25/10.44 exact (zenon_H1ee zenon_Hd3). % 10.25/10.44 apply (zenon_L523_); trivial. % 10.25/10.44 (* end of lemma zenon_L526_ *) % 10.25/10.44 assert (zenon_L527_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H3e zenon_H127. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H2d. zenon_intro zenon_H3f. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H2f. zenon_intro zenon_H83. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.25/10.44 exact (zenon_H1ea zenon_H127). % 10.25/10.44 (* end of lemma zenon_L527_ *) % 10.25/10.44 assert (zenon_L528_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1be zenon_H127. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_Hc3. zenon_intro zenon_H1bf. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H163. zenon_intro zenon_H83. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.25/10.44 exact (zenon_H1ea zenon_H127). % 10.25/10.44 (* end of lemma zenon_L528_ *) % 10.25/10.44 assert (zenon_L529_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1da zenon_H127 zenon_H1de. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_H13b. zenon_intro zenon_H1db. % 10.25/10.44 apply (zenon_L170_); trivial. % 10.25/10.44 (* end of lemma zenon_L529_ *) % 10.25/10.44 assert (zenon_L530_ : ((op (e3) (e2)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1ed zenon_H127 zenon_H2ef. % 10.25/10.44 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f1 ]. % 10.25/10.44 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e3) (e1)) = (op (e3) (e2)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2ef. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H1f0. % 10.25/10.44 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 10.25/10.44 cut (((op (e3) (e2)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f0]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e3) (e1)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2f0. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H1ed. % 10.25/10.44 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f1]. % 10.25/10.44 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 10.25/10.44 congruence. % 10.25/10.44 apply zenon_H1f1. apply refl_equal. % 10.25/10.44 apply zenon_H2f1. apply sym_equal. exact zenon_H127. % 10.25/10.44 apply zenon_H1f1. apply refl_equal. % 10.25/10.44 apply zenon_H1f1. apply refl_equal. % 10.25/10.44 (* end of lemma zenon_L530_ *) % 10.25/10.44 assert (zenon_L531_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1eb zenon_H127 zenon_H2ef. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ed. zenon_intro zenon_H1ec. % 10.25/10.44 apply (zenon_L530_); trivial. % 10.25/10.44 (* end of lemma zenon_L531_ *) % 10.25/10.44 assert (zenon_L532_ : ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H202 zenon_H171 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H99 zenon_H1de zenon_H2d zenon_Hc3 zenon_H2ef zenon_H127 zenon_H36 zenon_Hf4. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.25/10.44 apply (zenon_L1_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.25/10.44 apply (zenon_L2_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.25/10.44 apply (zenon_L3_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.25/10.44 apply (zenon_L4_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.25/10.44 apply (zenon_L5_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.25/10.44 apply (zenon_L6_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.25/10.44 apply (zenon_L512_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.25/10.44 apply (zenon_L527_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.25/10.44 apply (zenon_L10_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.25/10.44 apply (zenon_L513_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.25/10.44 apply (zenon_L13_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.25/10.44 apply (zenon_L495_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.25/10.44 apply (zenon_L15_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.25/10.44 apply (zenon_L497_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.25/10.44 apply (zenon_L498_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.25/10.44 apply (zenon_L19_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.25/10.44 apply (zenon_L20_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.25/10.44 apply (zenon_L21_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.25/10.44 apply (zenon_L499_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.25/10.44 apply (zenon_L500_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.25/10.44 apply (zenon_L24_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.25/10.44 apply (zenon_L25_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.25/10.44 apply (zenon_L26_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.25/10.44 apply (zenon_L27_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.25/10.44 apply (zenon_L501_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.25/10.44 apply (zenon_L31_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.25/10.44 apply (zenon_L32_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.25/10.44 apply (zenon_L502_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.25/10.44 apply (zenon_L503_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.25/10.44 apply (zenon_L56_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.25/10.44 apply (zenon_L106_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.25/10.44 apply (zenon_L147_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.25/10.44 apply (zenon_L148_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.25/10.44 apply (zenon_L505_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.25/10.44 apply (zenon_L150_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.25/10.44 apply (zenon_L514_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.25/10.44 apply (zenon_L509_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.25/10.44 apply (zenon_L154_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.25/10.44 apply (zenon_L155_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.25/10.44 apply (zenon_L528_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.25/10.44 apply (zenon_L157_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.25/10.44 apply (zenon_L158_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.25/10.44 apply (zenon_L159_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.25/10.44 apply (zenon_L160_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.25/10.44 apply (zenon_L516_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.25/10.44 apply (zenon_L517_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.25/10.44 apply (zenon_L164_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.25/10.44 apply (zenon_L165_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.25/10.44 apply (zenon_L166_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.25/10.44 apply (zenon_L518_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.25/10.44 apply (zenon_L529_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.25/10.44 apply (zenon_L169_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.25/10.44 apply (zenon_L520_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.25/10.44 apply (zenon_L172_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.25/10.44 apply (zenon_L521_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.25/10.44 apply (zenon_L174_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.25/10.44 apply (zenon_L531_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.25/10.44 apply (zenon_L369_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.25/10.44 apply (zenon_L178_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.25/10.44 apply (zenon_L179_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.25/10.44 apply (zenon_L180_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.25/10.44 apply (zenon_L181_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.25/10.44 apply (zenon_L182_); trivial. % 10.25/10.44 apply (zenon_L183_); trivial. % 10.25/10.44 (* end of lemma zenon_L532_ *) % 10.25/10.44 assert (zenon_L533_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H2f2 zenon_H2ed zenon_H79 zenon_H262 zenon_H154 zenon_H202 zenon_H171 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H99 zenon_H1de zenon_H2d zenon_Hc3 zenon_H2ef zenon_H36 zenon_Hf4. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2f2); [ zenon_intro zenon_H128 | zenon_intro zenon_H2f3 ]. % 10.25/10.44 apply (zenon_L525_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H175 | zenon_intro zenon_H2f4 ]. % 10.25/10.44 apply (zenon_L208_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H252 | zenon_intro zenon_H127 ]. % 10.25/10.44 apply (zenon_L333_); trivial. % 10.25/10.44 apply (zenon_L532_); trivial. % 10.25/10.44 (* end of lemma zenon_L533_ *) % 10.25/10.44 assert (zenon_L534_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H245 zenon_H26e zenon_H2cd zenon_H1eb zenon_H1ee zenon_H1e5 zenon_H2cf zenon_H1ed zenon_He9 zenon_H2f2 zenon_H2ed zenon_H262 zenon_H154 zenon_H202 zenon_H171 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H99 zenon_H1de zenon_H2d zenon_Hc3 zenon_H2ef zenon_H36 zenon_Hf4. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.44 apply (zenon_L524_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.44 apply (zenon_L526_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.44 apply (zenon_L185_); trivial. % 10.25/10.44 apply (zenon_L533_); trivial. % 10.25/10.44 (* end of lemma zenon_L534_ *) % 10.25/10.44 assert (zenon_L535_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H245 zenon_H26e zenon_H2cd zenon_H1eb zenon_H1e5 zenon_H2cf zenon_He9 zenon_H2f2 zenon_H2ed zenon_H262 zenon_H154 zenon_H202 zenon_H171 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H99 zenon_H1de zenon_H2d zenon_Hc3 zenon_H2ef zenon_H36 zenon_Hf4. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ed. zenon_intro zenon_H1ec. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ee. zenon_intro zenon_H43. % 10.25/10.44 apply (zenon_L534_); trivial. % 10.25/10.44 (* end of lemma zenon_L535_ *) % 10.25/10.44 assert (zenon_L536_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H2f5 zenon_Hc3 zenon_H171 zenon_H2d zenon_H2e4 zenon_H2e7 zenon_H36 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H99 zenon_He9 zenon_H104 zenon_Hfd zenon_H1de zenon_H12a zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_Hf4 zenon_H202 zenon_H154 zenon_H262 zenon_H245. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H127 ]. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.25/10.44 apply (zenon_L1_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.25/10.44 apply (zenon_L2_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.25/10.44 apply (zenon_L3_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.25/10.44 apply (zenon_L4_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.25/10.44 apply (zenon_L5_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.25/10.44 apply (zenon_L6_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.25/10.44 apply (zenon_L512_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.25/10.44 apply (zenon_L492_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.25/10.44 apply (zenon_L10_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.25/10.44 apply (zenon_L513_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.25/10.44 apply (zenon_L13_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.25/10.44 apply (zenon_L495_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.25/10.44 apply (zenon_L15_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.25/10.44 apply (zenon_L497_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.25/10.44 apply (zenon_L498_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.25/10.44 apply (zenon_L19_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.25/10.44 apply (zenon_L20_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.25/10.44 apply (zenon_L21_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.25/10.44 apply (zenon_L499_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.25/10.44 apply (zenon_L500_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.25/10.44 apply (zenon_L24_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.25/10.44 apply (zenon_L25_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.25/10.44 apply (zenon_L26_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.25/10.44 apply (zenon_L27_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.25/10.44 apply (zenon_L501_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.25/10.44 apply (zenon_L31_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.25/10.44 apply (zenon_L32_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.25/10.44 apply (zenon_L502_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.25/10.44 apply (zenon_L503_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.25/10.44 apply (zenon_L56_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.25/10.44 apply (zenon_L106_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.25/10.44 apply (zenon_L147_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.25/10.44 apply (zenon_L148_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.25/10.44 apply (zenon_L505_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.25/10.44 apply (zenon_L150_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.25/10.44 apply (zenon_L514_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.25/10.44 apply (zenon_L509_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.25/10.44 apply (zenon_L154_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.25/10.44 apply (zenon_L155_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.25/10.44 apply (zenon_L510_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.25/10.44 apply (zenon_L157_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.25/10.44 apply (zenon_L158_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.25/10.44 apply (zenon_L159_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.25/10.44 apply (zenon_L160_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.25/10.44 apply (zenon_L516_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.25/10.44 apply (zenon_L517_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.25/10.44 apply (zenon_L164_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.25/10.44 apply (zenon_L165_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.25/10.44 apply (zenon_L166_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.25/10.44 apply (zenon_L518_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.25/10.44 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_H13b. zenon_intro zenon_H1db. % 10.25/10.44 apply (zenon_L519_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.25/10.44 apply (zenon_L169_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.25/10.44 apply (zenon_L520_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.25/10.44 apply (zenon_L172_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.25/10.44 apply (zenon_L521_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.25/10.44 apply (zenon_L174_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.25/10.44 apply (zenon_L535_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.25/10.44 apply (zenon_L369_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.25/10.44 apply (zenon_L178_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.25/10.44 apply (zenon_L179_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.25/10.44 apply (zenon_L180_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.25/10.44 apply (zenon_L181_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.25/10.44 apply (zenon_L182_); trivial. % 10.25/10.44 apply (zenon_L183_); trivial. % 10.25/10.44 apply (zenon_L532_); trivial. % 10.25/10.44 (* end of lemma zenon_L536_ *) % 10.25/10.44 assert (zenon_L537_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H2bc zenon_H2e4 zenon_H2d zenon_H284 zenon_H198 zenon_Hdb zenon_Hda zenon_H17a. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H42 | zenon_intro zenon_H2bd ]. % 10.25/10.44 apply (zenon_L494_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H16e | zenon_intro zenon_H2be ]. % 10.25/10.44 apply (zenon_L258_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_Hcd | zenon_intro zenon_H150 ]. % 10.25/10.44 apply (zenon_L50_); trivial. % 10.25/10.44 apply (zenon_L308_); trivial. % 10.25/10.44 (* end of lemma zenon_L537_ *) % 10.25/10.44 assert (zenon_L538_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_H244 zenon_H130 zenon_H5a zenon_H252 zenon_Hfd zenon_H27c zenon_H150 zenon_H17c zenon_H29d. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.25/10.44 apply (zenon_L133_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.25/10.44 apply (zenon_L199_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.25/10.44 apply (zenon_L252_); trivial. % 10.25/10.44 apply (zenon_L395_); trivial. % 10.25/10.44 (* end of lemma zenon_L538_ *) % 10.25/10.44 assert (zenon_L539_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_Hdf zenon_H46 zenon_H104 zenon_Hff zenon_H2bc zenon_H2e4 zenon_H2d zenon_H284 zenon_H198 zenon_Hda zenon_H244 zenon_H130 zenon_H5a zenon_Hfd zenon_H27c zenon_H29d zenon_H2a8 zenon_H163 zenon_H36 zenon_H9c zenon_H293 zenon_H94 zenon_H17e zenon_H2f5 zenon_H171 zenon_H2e7 zenon_H177 zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H99 zenon_He9 zenon_H1de zenon_H12a zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_Hf4 zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H85 zenon_H2b9 zenon_Hd4 zenon_Hc6. % 10.25/10.44 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.44 apply (zenon_L511_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.44 apply (zenon_L310_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.44 apply (zenon_L486_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.44 apply (zenon_L310_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.44 apply (zenon_L536_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.44 apply (zenon_L359_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.44 apply (zenon_L225_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.44 apply (zenon_L537_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.25/10.44 apply (zenon_L258_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.25/10.44 apply (zenon_L36_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.25/10.44 exact (zenon_H163 zenon_H103). % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.25/10.44 apply (zenon_L538_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.25/10.44 apply (zenon_L537_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.25/10.44 exact (zenon_Hff zenon_Hfc). % 10.25/10.44 apply (zenon_L219_); trivial. % 10.25/10.44 apply (zenon_L238_); trivial. % 10.25/10.44 (* end of lemma zenon_L539_ *) % 10.25/10.44 assert (zenon_L540_ : ((op (e1) (e0)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (op (op (e0) (op (e0) (e0))) (e0)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_Hba zenon_H198 zenon_H5a zenon_H255. % 10.25/10.44 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.25/10.44 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((e2) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H255. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H256. % 10.25/10.44 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.25/10.44 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H258]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((op (e1) (e0)) = (e2)) = ((op (op (e0) (op (e0) (e0))) (e0)) = (e2))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H258. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_Hba. % 10.25/10.44 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.25/10.44 cut (((op (e1) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2f6]. % 10.25/10.44 congruence. % 10.25/10.44 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.25/10.44 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((op (e1) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2f6. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H256. % 10.25/10.44 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.25/10.44 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2f7]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.44 cut (((op (e0) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2f8]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (op (e0) (e0))) = (e1))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2f8. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H198. % 10.25/10.44 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.25/10.44 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2cb]. % 10.25/10.44 congruence. % 10.25/10.44 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.25/10.44 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e0) (e0))))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2cb. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H25d. % 10.25/10.44 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.25/10.44 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 10.25/10.44 congruence. % 10.25/10.44 apply (zenon_L381_); trivial. % 10.25/10.44 apply zenon_H25e. apply refl_equal. % 10.25/10.44 apply zenon_H25e. apply refl_equal. % 10.25/10.44 apply zenon_H98. apply refl_equal. % 10.25/10.44 apply zenon_H84. apply refl_equal. % 10.25/10.44 apply zenon_H257. apply refl_equal. % 10.25/10.44 apply zenon_H257. apply refl_equal. % 10.25/10.44 apply zenon_H87. apply refl_equal. % 10.25/10.44 apply zenon_H257. apply refl_equal. % 10.25/10.44 apply zenon_H257. apply refl_equal. % 10.25/10.44 (* end of lemma zenon_L540_ *) % 10.25/10.44 assert (zenon_L541_ : ((op (e1) (e0)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 10.25/10.44 do 0 intro. intros zenon_Hba zenon_H198 zenon_H5a. % 10.25/10.44 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_H197 | zenon_intro zenon_H2f9 ]. % 10.25/10.44 apply zenon_H197. apply sym_equal. exact zenon_H5a. % 10.25/10.44 apply (zenon_notand_s _ _ zenon_H2f9); [ zenon_intro zenon_H2fa | zenon_intro zenon_H255 ]. % 10.25/10.44 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.25/10.44 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e1) = (op (e0) (op (e0) (e0))))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2fa. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H25d. % 10.25/10.44 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.25/10.44 cut (((op (e0) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2f8]. % 10.25/10.44 congruence. % 10.25/10.44 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (op (e0) (e0))) = (e1))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2f8. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H198. % 10.25/10.44 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.25/10.44 cut (((op (e0) (e3)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2cb]. % 10.25/10.44 congruence. % 10.25/10.44 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.25/10.44 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e3)) = (op (e0) (op (e0) (e0))))). % 10.25/10.44 intro zenon_D_pnotp. % 10.25/10.44 apply zenon_H2cb. % 10.25/10.44 rewrite <- zenon_D_pnotp. % 10.25/10.44 exact zenon_H25d. % 10.25/10.44 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.25/10.44 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 10.25/10.44 congruence. % 10.25/10.44 apply (zenon_L381_); trivial. % 10.25/10.44 apply zenon_H25e. apply refl_equal. % 10.25/10.44 apply zenon_H25e. apply refl_equal. % 10.25/10.44 apply zenon_H98. apply refl_equal. % 10.25/10.44 apply zenon_H25e. apply refl_equal. % 10.25/10.44 apply zenon_H25e. apply refl_equal. % 10.25/10.44 apply (zenon_L540_); trivial. % 10.25/10.44 (* end of lemma zenon_L541_ *) % 10.25/10.44 assert (zenon_L542_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.25/10.44 do 0 intro. intros zenon_Hdf zenon_H5a zenon_H198 zenon_H36 zenon_Hf4 zenon_Hcd zenon_Hda zenon_Hd4 zenon_Hc6. % 10.25/10.44 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.44 apply (zenon_L541_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.44 apply (zenon_L310_); trivial. % 10.25/10.44 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.44 apply (zenon_L50_); trivial. % 10.25/10.44 apply (zenon_L238_); trivial. % 10.25/10.44 (* end of lemma zenon_L542_ *) % 10.25/10.44 assert (zenon_L543_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 10.25/10.44 do 0 intro. intros zenon_H1a3 zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_He9 zenon_H99 zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H177 zenon_H2e7 zenon_H171 zenon_H2f5 zenon_H17e zenon_H94 zenon_H293 zenon_H9c zenon_H163 zenon_H2a8 zenon_H29d zenon_H27c zenon_Hfd zenon_H130 zenon_H244 zenon_H284 zenon_H2e4 zenon_H2bc zenon_Hff zenon_H104 zenon_H85 zenon_H2d zenon_Hc6 zenon_Hd4 zenon_Hda zenon_Hf4 zenon_H36 zenon_H198 zenon_Hdf zenon_Hfa zenon_H5a. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.45 apply (zenon_L539_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.45 apply (zenon_L486_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.45 apply (zenon_L542_); trivial. % 10.25/10.45 apply (zenon_L383_); trivial. % 10.25/10.45 (* end of lemma zenon_L543_ *) % 10.25/10.45 assert (zenon_L544_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> False). % 10.25/10.45 do 0 intro. intros zenon_He0 zenon_Hc0 zenon_H46 zenon_Hfd zenon_H120 zenon_H182 zenon_Hdb zenon_Hf4 zenon_H107. % 10.25/10.45 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.45 apply (zenon_L88_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.45 apply (zenon_L73_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.45 apply (zenon_L307_); trivial. % 10.25/10.45 apply (zenon_L269_); trivial. % 10.25/10.45 (* end of lemma zenon_L544_ *) % 10.25/10.45 assert (zenon_L545_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.45 do 0 intro. intros zenon_H2b9 zenon_H85 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_Hf4 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_H104 zenon_He9 zenon_H99 zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H36 zenon_H2e7 zenon_H2e4 zenon_H2d zenon_H171 zenon_H2f5 zenon_Hfd zenon_H127. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.45 apply (zenon_L486_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.45 apply (zenon_L310_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.45 apply (zenon_L536_); trivial. % 10.25/10.45 apply (zenon_L199_); trivial. % 10.25/10.45 (* end of lemma zenon_L545_ *) % 10.25/10.45 assert (zenon_L546_ : (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.25/10.45 do 0 intro. intros zenon_Hfd zenon_H2f5 zenon_H171 zenon_H2d zenon_H2e4 zenon_H2e7 zenon_H36 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H99 zenon_He9 zenon_H104 zenon_H1de zenon_H12a zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_Hf4 zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H85 zenon_H2b9 zenon_H298 zenon_H5a zenon_Hfa zenon_Hdf zenon_Hda zenon_Hff zenon_H2bc zenon_H284 zenon_H244 zenon_H130 zenon_H27c zenon_H29d zenon_H2a8 zenon_H163 zenon_H293 zenon_H94 zenon_H17e zenon_H1a3 zenon_H182 zenon_H46 zenon_Hc0 zenon_He0 zenon_H1e5 zenon_Hd4 zenon_Hc6. % 10.25/10.45 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.45 apply (zenon_L511_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.45 apply (zenon_L310_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.25/10.45 apply (zenon_L134_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.25/10.45 apply (zenon_L225_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.25/10.45 apply (zenon_L543_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.25/10.45 apply (zenon_L65_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.25/10.45 apply (zenon_L544_); trivial. % 10.25/10.45 exact (zenon_H1e5 zenon_H189). % 10.25/10.45 apply (zenon_L545_); trivial. % 10.25/10.45 apply (zenon_L238_); trivial. % 10.25/10.45 (* end of lemma zenon_L546_ *) % 10.25/10.45 assert (zenon_L547_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.45 do 0 intro. intros zenon_H298 zenon_Hc6 zenon_Hda zenon_Hcd zenon_H36 zenon_H5a zenon_Hdf zenon_Ha5 zenon_H99 zenon_Hd4 zenon_Hf4 zenon_H1e5. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.25/10.45 apply (zenon_L542_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.25/10.45 apply (zenon_L71_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.25/10.45 apply (zenon_L269_); trivial. % 10.25/10.45 exact (zenon_H1e5 zenon_H189). % 10.25/10.45 (* end of lemma zenon_L547_ *) % 10.25/10.45 assert (zenon_L548_ : (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> ((op (e3) (e3)) = (e0)) -> False). % 10.25/10.45 do 0 intro. intros zenon_He9 zenon_H67 zenon_H79. % 10.25/10.45 cut (((op (e3) (e3)) = (e3)) = ((e0) = (e3))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_He9. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H67. % 10.25/10.45 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.25/10.45 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 10.25/10.45 congruence. % 10.25/10.45 exact (zenon_H76 zenon_H79). % 10.25/10.45 apply zenon_Heb. apply refl_equal. % 10.25/10.45 (* end of lemma zenon_L548_ *) % 10.25/10.45 assert (zenon_L549_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> False). % 10.25/10.45 do 0 intro. intros zenon_H244 zenon_H130 zenon_H5a zenon_H252 zenon_Hfd zenon_H186 zenon_H17a zenon_He9 zenon_H79. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.25/10.45 apply (zenon_L133_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.25/10.45 apply (zenon_L199_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.25/10.45 apply (zenon_L249_); trivial. % 10.25/10.45 apply (zenon_L548_); trivial. % 10.25/10.45 (* end of lemma zenon_L549_ *) % 10.25/10.45 assert (zenon_L550_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.25/10.45 do 0 intro. intros zenon_H272 zenon_H59 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_Hdf zenon_H36 zenon_Hcd zenon_Hda zenon_Hc6 zenon_H298 zenon_Hd4 zenon_H85 zenon_H244 zenon_H130 zenon_H5a zenon_H252 zenon_Hfd zenon_H186 zenon_H17a zenon_He9. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.45 exact (zenon_H59 zenon_H56). % 10.25/10.45 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.45 apply (zenon_L547_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.45 apply (zenon_L234_); trivial. % 10.25/10.45 apply (zenon_L549_); trivial. % 10.25/10.45 (* end of lemma zenon_L550_ *) % 10.25/10.45 assert (zenon_L551_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.45 do 0 intro. intros zenon_H298 zenon_H284 zenon_H16e zenon_H104 zenon_H17c zenon_Hd4 zenon_Hf4 zenon_H1e5. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.25/10.45 apply (zenon_L258_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.25/10.45 apply (zenon_L341_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.25/10.45 apply (zenon_L269_); trivial. % 10.25/10.45 exact (zenon_H1e5 zenon_H189). % 10.25/10.45 (* end of lemma zenon_L551_ *) % 10.25/10.45 assert (zenon_L552_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.45 do 0 intro. intros zenon_H17e zenon_H94 zenon_He9 zenon_H186 zenon_Hfd zenon_H252 zenon_H5a zenon_H130 zenon_H244 zenon_H85 zenon_Hc6 zenon_Hda zenon_Hcd zenon_H36 zenon_Hdf zenon_H99 zenon_H59 zenon_H272 zenon_H298 zenon_H284 zenon_H16e zenon_H104 zenon_Hd4 zenon_Hf4 zenon_H1e5. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.45 apply (zenon_L359_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.45 apply (zenon_L225_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.45 apply (zenon_L550_); trivial. % 10.25/10.45 apply (zenon_L551_); trivial. % 10.25/10.45 (* end of lemma zenon_L552_ *) % 10.25/10.45 assert (zenon_L553_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.45 do 0 intro. intros zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H2d zenon_H171 zenon_H2f5 zenon_H17e zenon_H94 zenon_He9 zenon_H186 zenon_Hfd zenon_H5a zenon_H130 zenon_H244 zenon_H85 zenon_Hc6 zenon_Hda zenon_Hcd zenon_H36 zenon_Hdf zenon_H99 zenon_H59 zenon_H272 zenon_H298 zenon_H284 zenon_H16e zenon_H104 zenon_Hd4 zenon_Hf4 zenon_H1e5. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.45 apply (zenon_L486_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.45 apply (zenon_L310_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.45 apply (zenon_L536_); trivial. % 10.25/10.45 apply (zenon_L552_); trivial. % 10.25/10.45 (* end of lemma zenon_L553_ *) % 10.25/10.45 assert (zenon_L554_ : (~((op (e0) (op (e0) (e0))) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e2)) -> False). % 10.25/10.45 do 0 intro. intros zenon_H2fb zenon_H46. % 10.25/10.45 cut (((op (e0) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 10.25/10.45 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.45 congruence. % 10.25/10.45 apply zenon_H84. apply refl_equal. % 10.25/10.45 exact (zenon_H44 zenon_H46). % 10.25/10.45 (* end of lemma zenon_L554_ *) % 10.25/10.45 assert (zenon_L555_ : ((op (e1) (e0)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((e3) = (op (op (e0) (op (e0) (e0))) (e0)))) -> False). % 10.25/10.45 do 0 intro. intros zenon_H13c zenon_H16e zenon_H46 zenon_H2b2. % 10.25/10.45 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((e3) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H2b2. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H256. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2b3]. % 10.25/10.45 congruence. % 10.25/10.45 cut (((op (e1) (e0)) = (e3)) = ((op (op (e0) (op (e0) (e0))) (e0)) = (e3))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H2b3. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H13c. % 10.25/10.45 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.25/10.45 cut (((op (e1) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2f6]. % 10.25/10.45 congruence. % 10.25/10.45 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((op (e1) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H2f6. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H256. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H2f7]. % 10.25/10.45 congruence. % 10.25/10.45 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2f8]. % 10.25/10.45 congruence. % 10.25/10.45 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (op (e0) (e0))) = (e1))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H2f8. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H16e. % 10.25/10.45 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.25/10.45 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2fc]. % 10.25/10.45 congruence. % 10.25/10.45 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e0) (e0))))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H2fc. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H25d. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2fb]. % 10.25/10.45 congruence. % 10.25/10.45 apply (zenon_L554_); trivial. % 10.25/10.45 apply zenon_H25e. apply refl_equal. % 10.25/10.45 apply zenon_H25e. apply refl_equal. % 10.25/10.45 apply zenon_H98. apply refl_equal. % 10.25/10.45 apply zenon_H84. apply refl_equal. % 10.25/10.45 apply zenon_H257. apply refl_equal. % 10.25/10.45 apply zenon_H257. apply refl_equal. % 10.25/10.45 apply zenon_Heb. apply refl_equal. % 10.25/10.45 apply zenon_H257. apply refl_equal. % 10.25/10.45 apply zenon_H257. apply refl_equal. % 10.25/10.45 (* end of lemma zenon_L555_ *) % 10.25/10.45 assert (zenon_L556_ : ((op (e1) (e0)) = (e3)) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> False). % 10.25/10.45 do 0 intro. intros zenon_H13c zenon_H16e zenon_H46. % 10.25/10.45 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H149 | zenon_intro zenon_H2fd ]. % 10.25/10.45 apply zenon_H149. apply sym_equal. exact zenon_H46. % 10.25/10.45 apply (zenon_notand_s _ _ zenon_H2fd); [ zenon_intro zenon_H2fa | zenon_intro zenon_H2b2 ]. % 10.25/10.45 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e1) = (op (e0) (op (e0) (e0))))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H2fa. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H25d. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2f8]. % 10.25/10.45 congruence. % 10.25/10.45 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (op (e0) (e0))) = (e1))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H2f8. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H16e. % 10.25/10.45 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.25/10.45 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2fc]. % 10.25/10.45 congruence. % 10.25/10.45 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e0) (e0))))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H2fc. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H25d. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2fb]. % 10.25/10.45 congruence. % 10.25/10.45 apply (zenon_L554_); trivial. % 10.25/10.45 apply zenon_H25e. apply refl_equal. % 10.25/10.45 apply zenon_H25e. apply refl_equal. % 10.25/10.45 apply zenon_H98. apply refl_equal. % 10.25/10.45 apply zenon_H25e. apply refl_equal. % 10.25/10.45 apply zenon_H25e. apply refl_equal. % 10.25/10.45 apply (zenon_L555_); trivial. % 10.25/10.45 (* end of lemma zenon_L556_ *) % 10.25/10.45 assert (zenon_L557_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.25/10.45 do 0 intro. intros zenon_H293 zenon_H284 zenon_H198 zenon_H9c zenon_H36 zenon_H287 zenon_Hfa zenon_H104 zenon_H1ed. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.25/10.45 apply (zenon_L258_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.25/10.45 apply (zenon_L36_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.25/10.45 apply (zenon_L260_); trivial. % 10.25/10.45 apply (zenon_L219_); trivial. % 10.25/10.45 (* end of lemma zenon_L557_ *) % 10.25/10.45 assert (zenon_L558_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.25/10.45 do 0 intro. intros zenon_H191 zenon_Hf4 zenon_H46 zenon_H177 zenon_H1ed zenon_H104 zenon_H287 zenon_H36 zenon_H9c zenon_H198 zenon_H284 zenon_H293 zenon_H131 zenon_H99. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.25/10.45 apply (zenon_L57_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.25/10.45 apply (zenon_L282_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.25/10.45 apply (zenon_L557_); trivial. % 10.25/10.45 apply (zenon_L110_); trivial. % 10.25/10.45 (* end of lemma zenon_L558_ *) % 10.25/10.45 assert (zenon_L559_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> False). % 10.25/10.45 do 0 intro. intros zenon_H1a3 zenon_H2b9 zenon_H2ea zenon_H1c9 zenon_H17e zenon_H94 zenon_H2e4 zenon_H2bc zenon_H244 zenon_H130 zenon_Hfd zenon_H99 zenon_H131 zenon_H293 zenon_H284 zenon_H9c zenon_H287 zenon_H104 zenon_H177 zenon_H191 zenon_H29d zenon_H85 zenon_H2d zenon_Hc6 zenon_Hd4 zenon_Hda zenon_Hf4 zenon_H36 zenon_H198 zenon_Hdf zenon_Hfa zenon_H5a. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.45 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.45 apply (zenon_L511_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.45 apply (zenon_L310_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.45 apply (zenon_L486_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.45 apply (zenon_L310_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.45 apply (zenon_L516_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.45 apply (zenon_L359_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.45 apply (zenon_L225_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.45 apply (zenon_L537_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.25/10.45 apply (zenon_L133_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.25/10.45 apply (zenon_L199_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.25/10.45 apply (zenon_L558_); trivial. % 10.25/10.45 apply (zenon_L395_); trivial. % 10.25/10.45 apply (zenon_L238_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.45 apply (zenon_L486_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.45 apply (zenon_L542_); trivial. % 10.25/10.45 apply (zenon_L383_); trivial. % 10.25/10.45 (* end of lemma zenon_L559_ *) % 10.25/10.45 assert (zenon_L560_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.45 do 0 intro. intros zenon_H298 zenon_H5a zenon_Hfa zenon_Hdf zenon_H36 zenon_Hda zenon_Hc6 zenon_H2d zenon_H85 zenon_H29d zenon_H191 zenon_H177 zenon_H104 zenon_H287 zenon_H9c zenon_H284 zenon_H293 zenon_H131 zenon_Hfd zenon_H130 zenon_H244 zenon_H2bc zenon_H2e4 zenon_H94 zenon_H17e zenon_H1c9 zenon_H2ea zenon_H2b9 zenon_H1a3 zenon_Ha5 zenon_H99 zenon_Hd4 zenon_Hf4 zenon_H1e5. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.25/10.45 apply (zenon_L559_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.25/10.45 apply (zenon_L71_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.25/10.45 apply (zenon_L269_); trivial. % 10.25/10.45 exact (zenon_H1e5 zenon_H189). % 10.25/10.45 (* end of lemma zenon_L560_ *) % 10.25/10.45 assert (zenon_L561_ : (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.45 do 0 intro. intros zenon_He9 zenon_H186 zenon_Hfd zenon_H252 zenon_H5a zenon_H130 zenon_H244 zenon_H85 zenon_Hfa zenon_Hdf zenon_H36 zenon_Hda zenon_Hc6 zenon_H2d zenon_H29d zenon_H191 zenon_H177 zenon_H287 zenon_H9c zenon_H293 zenon_H131 zenon_H2bc zenon_H2e4 zenon_H94 zenon_H17e zenon_H1c9 zenon_H2ea zenon_H2b9 zenon_H1a3 zenon_H99 zenon_H59 zenon_H272 zenon_H298 zenon_H284 zenon_H16e zenon_H104 zenon_Hd4 zenon_Hf4 zenon_H1e5. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.45 apply (zenon_L359_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.45 apply (zenon_L225_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.45 exact (zenon_H59 zenon_H56). % 10.25/10.45 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.45 apply (zenon_L560_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.45 apply (zenon_L234_); trivial. % 10.25/10.45 apply (zenon_L549_); trivial. % 10.25/10.45 apply (zenon_L551_); trivial. % 10.25/10.45 (* end of lemma zenon_L561_ *) % 10.25/10.45 assert (zenon_L562_ : (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e0)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.45 do 0 intro. intros zenon_He9 zenon_H186 zenon_Hfd zenon_H5a zenon_H130 zenon_H244 zenon_H85 zenon_Hfa zenon_Hdf zenon_H36 zenon_Hda zenon_Hc6 zenon_H2d zenon_H29d zenon_H191 zenon_H177 zenon_H287 zenon_H9c zenon_H293 zenon_H131 zenon_H2bc zenon_H2e4 zenon_H94 zenon_H17e zenon_H1c9 zenon_H2ea zenon_H2b9 zenon_H1a3 zenon_H99 zenon_H59 zenon_H272 zenon_H298 zenon_H284 zenon_H16e zenon_H104 zenon_Hd4 zenon_Hf4 zenon_H1e5. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.45 apply (zenon_L486_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.45 apply (zenon_L310_); trivial. % 10.25/10.45 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.45 apply (zenon_L516_); trivial. % 10.25/10.45 apply (zenon_L561_); trivial. % 10.25/10.45 (* end of lemma zenon_L562_ *) % 10.25/10.45 assert (zenon_L563_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 10.25/10.45 do 0 intro. intros zenon_H14b zenon_H2d zenon_H128. % 10.25/10.45 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H14b. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H2d. % 10.25/10.45 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26d]. % 10.25/10.45 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 10.25/10.45 congruence. % 10.25/10.45 apply zenon_H39. apply refl_equal. % 10.25/10.45 apply zenon_H26d. apply sym_equal. exact zenon_H128. % 10.25/10.45 (* end of lemma zenon_L563_ *) % 10.25/10.45 assert (zenon_L564_ : ((op (e3) (e0)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> (~((e1) = (op (op (e0) (op (e0) (e0))) (e0)))) -> False). % 10.25/10.45 do 0 intro. intros zenon_H133 zenon_H150 zenon_H46 zenon_H2c9. % 10.25/10.45 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((e1) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H2c9. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H256. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H2ca]. % 10.25/10.45 congruence. % 10.25/10.45 cut (((op (e3) (e0)) = (e1)) = ((op (op (e0) (op (e0) (e0))) (e0)) = (e1))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H2ca. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H133. % 10.25/10.45 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.25/10.45 cut (((op (e3) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 10.25/10.45 congruence. % 10.25/10.45 elim (classic ((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [ zenon_intro zenon_H256 | zenon_intro zenon_H257 ]. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0))) = ((op (e3) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H259. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H256. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (op (e0) (op (e0) (e0))) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 10.25/10.45 cut (((op (op (e0) (op (e0) (e0))) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 10.25/10.45 congruence. % 10.25/10.45 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H25b]. % 10.25/10.45 congruence. % 10.25/10.45 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (op (e0) (e0))) = (e3))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H25b. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H150. % 10.25/10.45 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.25/10.45 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2fc]. % 10.25/10.45 congruence. % 10.25/10.45 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e0) (e0))))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.45 apply zenon_H2fc. % 10.25/10.45 rewrite <- zenon_D_pnotp. % 10.25/10.45 exact zenon_H25d. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2fb]. % 10.25/10.45 congruence. % 10.25/10.45 apply (zenon_L554_); trivial. % 10.25/10.45 apply zenon_H25e. apply refl_equal. % 10.25/10.45 apply zenon_H25e. apply refl_equal. % 10.25/10.45 apply zenon_Heb. apply refl_equal. % 10.25/10.45 apply zenon_H84. apply refl_equal. % 10.25/10.45 apply zenon_H257. apply refl_equal. % 10.25/10.45 apply zenon_H257. apply refl_equal. % 10.25/10.45 apply zenon_H98. apply refl_equal. % 10.25/10.45 apply zenon_H257. apply refl_equal. % 10.25/10.45 apply zenon_H257. apply refl_equal. % 10.25/10.45 (* end of lemma zenon_L564_ *) % 10.25/10.45 assert (zenon_L565_ : ((op (e3) (e0)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e0)) = (e2)) -> False). % 10.25/10.45 do 0 intro. intros zenon_H133 zenon_H150 zenon_H46. % 10.25/10.45 apply (zenon_notand_s _ _ ax9); [ zenon_intro zenon_H149 | zenon_intro zenon_H2fe ]. % 10.25/10.45 apply zenon_H149. apply sym_equal. exact zenon_H46. % 10.25/10.45 apply (zenon_notand_s _ _ zenon_H2fe); [ zenon_intro zenon_H261 | zenon_intro zenon_H2c9 ]. % 10.25/10.45 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.25/10.45 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((e3) = (op (e0) (op (e0) (e0))))). % 10.25/10.45 intro zenon_D_pnotp. % 10.25/10.46 apply zenon_H261. % 10.25/10.46 rewrite <- zenon_D_pnotp. % 10.25/10.46 exact zenon_H25d. % 10.25/10.46 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.25/10.46 cut (((op (e0) (op (e0) (e0))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H25b]. % 10.25/10.46 congruence. % 10.25/10.46 cut (((op (e0) (e2)) = (e3)) = ((op (e0) (op (e0) (e0))) = (e3))). % 10.25/10.46 intro zenon_D_pnotp. % 10.25/10.46 apply zenon_H25b. % 10.25/10.46 rewrite <- zenon_D_pnotp. % 10.25/10.46 exact zenon_H150. % 10.25/10.46 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.25/10.46 cut (((op (e0) (e2)) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H2fc]. % 10.25/10.46 congruence. % 10.25/10.46 elim (classic ((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [ zenon_intro zenon_H25d | zenon_intro zenon_H25e ]. % 10.25/10.46 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0)))) = ((op (e0) (e2)) = (op (e0) (op (e0) (e0))))). % 10.25/10.46 intro zenon_D_pnotp. % 10.25/10.46 apply zenon_H2fc. % 10.25/10.46 rewrite <- zenon_D_pnotp. % 10.25/10.46 exact zenon_H25d. % 10.25/10.46 cut (((op (e0) (op (e0) (e0))) = (op (e0) (op (e0) (e0))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 10.25/10.46 cut (((op (e0) (op (e0) (e0))) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2fb]. % 10.25/10.46 congruence. % 10.25/10.46 apply (zenon_L554_); trivial. % 10.25/10.46 apply zenon_H25e. apply refl_equal. % 10.25/10.46 apply zenon_H25e. apply refl_equal. % 10.25/10.46 apply zenon_Heb. apply refl_equal. % 10.25/10.46 apply zenon_H25e. apply refl_equal. % 10.25/10.46 apply zenon_H25e. apply refl_equal. % 10.25/10.46 apply (zenon_L564_); trivial. % 10.25/10.46 (* end of lemma zenon_L565_ *) % 10.25/10.46 assert (zenon_L566_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 10.25/10.46 do 0 intro. intros zenon_H2bc zenon_H241 zenon_H27c zenon_H284 zenon_Hc6 zenon_Hd4 zenon_Hf4 zenon_H36 zenon_H198 zenon_H5a zenon_Hdf zenon_Hda zenon_H17a. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H42 | zenon_intro zenon_H2bd ]. % 10.25/10.46 apply (zenon_L322_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H16e | zenon_intro zenon_H2be ]. % 10.25/10.46 apply (zenon_L258_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_Hcd | zenon_intro zenon_H150 ]. % 10.25/10.46 apply (zenon_L542_); trivial. % 10.25/10.46 apply (zenon_L308_); trivial. % 10.25/10.46 (* end of lemma zenon_L566_ *) % 10.25/10.46 assert (zenon_L567_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> False). % 10.25/10.46 do 0 intro. intros zenon_H2a8 zenon_H46 zenon_H133 zenon_Hda zenon_Hdf zenon_H5a zenon_H198 zenon_H36 zenon_Hf4 zenon_Hd4 zenon_Hc6 zenon_H284 zenon_H27c zenon_H2bc zenon_Hff zenon_He9 zenon_H241. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.25/10.46 apply (zenon_L565_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.25/10.46 apply (zenon_L566_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.25/10.46 exact (zenon_Hff zenon_Hfc). % 10.25/10.46 apply (zenon_L185_); trivial. % 10.25/10.46 (* end of lemma zenon_L567_ *) % 10.25/10.46 assert (zenon_L568_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H298 zenon_H241 zenon_He9 zenon_Hff zenon_H2bc zenon_H27c zenon_H284 zenon_Hc6 zenon_H36 zenon_H5a zenon_Hdf zenon_Hda zenon_H133 zenon_H46 zenon_H2a8 zenon_Ha5 zenon_H99 zenon_Hd4 zenon_Hf4 zenon_H1e5. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.25/10.46 apply (zenon_L567_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.25/10.46 apply (zenon_L71_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.25/10.46 apply (zenon_L269_); trivial. % 10.25/10.46 exact (zenon_H1e5 zenon_H189). % 10.25/10.46 (* end of lemma zenon_L568_ *) % 10.25/10.46 assert (zenon_L569_ : (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H1e5 zenon_Hf4 zenon_Hd4 zenon_H104 zenon_H16e zenon_H284 zenon_H298 zenon_H272 zenon_H59 zenon_H1a3 zenon_H2b9 zenon_H2ea zenon_H1c9 zenon_H17e zenon_H94 zenon_H2e4 zenon_H2bc zenon_H293 zenon_H9c zenon_H287 zenon_H177 zenon_H191 zenon_H29d zenon_H2d zenon_Hc6 zenon_Hda zenon_H36 zenon_Hdf zenon_H85 zenon_H244 zenon_H130 zenon_H5a zenon_Hfd zenon_H186 zenon_He9 zenon_H131 zenon_H99. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.25/10.46 apply (zenon_L295_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.25/10.46 apply (zenon_L282_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.25/10.46 apply (zenon_L562_); trivial. % 10.25/10.46 apply (zenon_L110_); trivial. % 10.25/10.46 (* end of lemma zenon_L569_ *) % 10.25/10.46 assert (zenon_L570_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H245 zenon_H85 zenon_H29d zenon_H191 zenon_H177 zenon_H287 zenon_H9c zenon_H293 zenon_H2e4 zenon_H94 zenon_H17e zenon_H1c9 zenon_H2ea zenon_H2b9 zenon_H1a3 zenon_H59 zenon_H272 zenon_H16e zenon_H104 zenon_H2d zenon_H14b zenon_H1e5 zenon_Hf4 zenon_Hd4 zenon_H99 zenon_Ha5 zenon_H2a8 zenon_H46 zenon_H133 zenon_Hda zenon_Hdf zenon_H36 zenon_Hc6 zenon_H284 zenon_H27c zenon_H2bc zenon_Hff zenon_H298 zenon_H244 zenon_H130 zenon_H5a zenon_H252 zenon_Hfd zenon_H186 zenon_H17a zenon_He9. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.46 apply (zenon_L569_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.46 apply (zenon_L563_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.46 apply (zenon_L568_); trivial. % 10.25/10.46 apply (zenon_L549_); trivial. % 10.25/10.46 (* end of lemma zenon_L570_ *) % 10.25/10.46 assert (zenon_L571_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e0)) -> False). % 10.25/10.46 do 0 intro. intros zenon_He0 zenon_Hc0 zenon_H46 zenon_H101 zenon_Hf4 zenon_H182 zenon_Hdb zenon_H85 zenon_Hc7. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.46 apply (zenon_L88_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.46 apply (zenon_L193_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.46 apply (zenon_L307_); trivial. % 10.25/10.46 apply (zenon_L234_); trivial. % 10.25/10.46 (* end of lemma zenon_L571_ *) % 10.25/10.46 assert (zenon_L572_ : (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H163 zenon_Hff zenon_H2bc zenon_H27c zenon_Hc6 zenon_H36 zenon_Hdf zenon_Hda zenon_H133 zenon_H2a8 zenon_H99 zenon_H14b zenon_H2d zenon_H272 zenon_H59 zenon_H1a3 zenon_H2b9 zenon_H2ea zenon_H1c9 zenon_H17e zenon_H94 zenon_H2e4 zenon_H293 zenon_H9c zenon_H287 zenon_H177 zenon_H191 zenon_H29d zenon_H245 zenon_H85 zenon_Hdb zenon_H182 zenon_H46 zenon_Hc0 zenon_He0 zenon_H244 zenon_H130 zenon_H5a zenon_H252 zenon_Hfd zenon_H186 zenon_He9 zenon_H124 zenon_H298 zenon_H284 zenon_H16e zenon_H104 zenon_Hd4 zenon_Hf4 zenon_H1e5. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.46 apply (zenon_L556_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.46 apply (zenon_L225_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.46 apply (zenon_L562_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.46 apply (zenon_L563_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.46 exact (zenon_H59 zenon_H56). % 10.25/10.46 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.46 apply (zenon_L568_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.46 apply (zenon_L234_); trivial. % 10.25/10.46 apply (zenon_L549_); trivial. % 10.25/10.46 apply (zenon_L549_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.46 exact (zenon_H59 zenon_H56). % 10.25/10.46 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.46 apply (zenon_L570_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.46 apply (zenon_L571_); trivial. % 10.25/10.46 apply (zenon_L549_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.46 exact (zenon_H163 zenon_H103). % 10.25/10.46 apply (zenon_L269_); trivial. % 10.25/10.46 apply (zenon_L551_); trivial. % 10.25/10.46 (* end of lemma zenon_L572_ *) % 10.25/10.46 assert (zenon_L573_ : (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H163 zenon_Hff zenon_H2bc zenon_H27c zenon_H133 zenon_H2a8 zenon_H14b zenon_H1a3 zenon_H1c9 zenon_H293 zenon_H287 zenon_H191 zenon_H29d zenon_H182 zenon_Hc0 zenon_He0 zenon_H124 zenon_H1e5 zenon_Hf4 zenon_H104 zenon_H16e zenon_H284 zenon_H298 zenon_H272 zenon_H59 zenon_H99 zenon_Hdf zenon_H36 zenon_Hda zenon_Hc6 zenon_H85 zenon_H244 zenon_H130 zenon_H5a zenon_Hfd zenon_H186 zenon_He9 zenon_H94 zenon_H17e zenon_H2f5 zenon_H171 zenon_H2d zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H1de zenon_H12a zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_Hd4 zenon_H157. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.46 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.46 apply (zenon_L511_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.46 apply (zenon_L310_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.46 apply (zenon_L486_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.46 apply (zenon_L310_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.46 apply (zenon_L516_); trivial. % 10.25/10.46 apply (zenon_L572_); trivial. % 10.25/10.46 apply (zenon_L238_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.46 apply (zenon_L486_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.46 apply (zenon_L553_); trivial. % 10.25/10.46 apply (zenon_L240_); trivial. % 10.25/10.46 (* end of lemma zenon_L573_ *) % 10.25/10.46 assert (zenon_L574_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H1a2 zenon_H157 zenon_H186 zenon_H272 zenon_H298 zenon_H1e5 zenon_H124 zenon_He0 zenon_Hc0 zenon_H182 zenon_H191 zenon_H287 zenon_H1c9 zenon_H14b zenon_H1a3 zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_He9 zenon_H99 zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H177 zenon_H2e7 zenon_H171 zenon_H2f5 zenon_H17e zenon_H94 zenon_H293 zenon_H9c zenon_H163 zenon_H2a8 zenon_H29d zenon_H27c zenon_Hfd zenon_H130 zenon_H244 zenon_H284 zenon_H2e4 zenon_H2bc zenon_H104 zenon_H85 zenon_H2d zenon_Hc6 zenon_Hda zenon_H36 zenon_Hdf zenon_Hf4. % 10.25/10.46 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_Hd4. zenon_intro zenon_H1ca. % 10.25/10.46 apply (zenon_and_s _ _ zenon_H1ca). zenon_intro zenon_Hff. zenon_intro zenon_H57. % 10.25/10.46 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.25/10.46 apply (zenon_L295_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.25/10.46 apply (zenon_L58_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.25/10.46 apply (zenon_L295_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.25/10.46 apply (zenon_L282_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.46 apply (zenon_L546_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.46 apply (zenon_L486_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.46 apply (zenon_L553_); trivial. % 10.25/10.46 apply (zenon_L383_); trivial. % 10.25/10.46 apply (zenon_L573_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.46 apply (zenon_L539_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.46 apply (zenon_L486_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.46 apply (zenon_L542_); trivial. % 10.25/10.46 apply (zenon_L143_); trivial. % 10.25/10.46 (* end of lemma zenon_L574_ *) % 10.25/10.46 assert (zenon_L575_ : (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> False). % 10.25/10.46 do 0 intro. intros zenon_He9 zenon_H13b zenon_H131. % 10.25/10.46 cut (((op (e3) (e0)) = (e3)) = ((e0) = (e3))). % 10.25/10.46 intro zenon_D_pnotp. % 10.25/10.46 apply zenon_He9. % 10.25/10.46 rewrite <- zenon_D_pnotp. % 10.25/10.46 exact zenon_H13b. % 10.25/10.46 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.25/10.46 cut (((op (e3) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H2ff]. % 10.25/10.46 congruence. % 10.25/10.46 exact (zenon_H2ff zenon_H131). % 10.25/10.46 apply zenon_Heb. apply refl_equal. % 10.25/10.46 (* end of lemma zenon_L575_ *) % 10.25/10.46 assert (zenon_L576_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H245 zenon_H13b zenon_He9 zenon_H2d zenon_H14b zenon_H74 zenon_H278 zenon_H76. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.46 apply (zenon_L575_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.46 apply (zenon_L563_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.46 apply (zenon_L298_); trivial. % 10.25/10.46 exact (zenon_H76 zenon_H79). % 10.25/10.46 (* end of lemma zenon_L576_ *) % 10.25/10.46 assert (zenon_L577_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> (~((op (e2) (e2)) = (e1))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H1e6 zenon_H163. % 10.25/10.46 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H127. zenon_intro zenon_H1e7. % 10.25/10.46 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1e5. zenon_intro zenon_H80. % 10.25/10.46 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.25/10.46 exact (zenon_H163 zenon_H103). % 10.25/10.46 (* end of lemma zenon_L577_ *) % 10.25/10.46 assert (zenon_L578_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H17e zenon_H46 zenon_H186 zenon_He0 zenon_Hc1 zenon_H85 zenon_H36 zenon_H2ef zenon_H2d zenon_H1de zenon_H99 zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H171 zenon_H202 zenon_H154 zenon_H262 zenon_H2ed zenon_H2f2 zenon_He9 zenon_H1ed zenon_H2cf zenon_H1ee zenon_H1eb zenon_H2cd zenon_H26e zenon_H245 zenon_H182 zenon_Hdb zenon_H298 zenon_H284 zenon_H16e zenon_H104 zenon_Hf4 zenon_H1e5. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.46 apply (zenon_L556_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.46 apply (zenon_L225_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.46 apply (zenon_L249_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.46 apply (zenon_L417_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.46 apply (zenon_L534_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.46 apply (zenon_L307_); trivial. % 10.25/10.46 apply (zenon_L551_); trivial. % 10.25/10.46 (* end of lemma zenon_L578_ *) % 10.25/10.46 assert (zenon_L579_ : ((op (e3) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H79 zenon_Ha5 zenon_H29d. % 10.25/10.46 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.25/10.46 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 10.25/10.46 intro zenon_D_pnotp. % 10.25/10.46 apply zenon_H29d. % 10.25/10.46 rewrite <- zenon_D_pnotp. % 10.25/10.46 exact zenon_Hd6. % 10.25/10.46 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.25/10.46 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H29e]. % 10.25/10.46 congruence. % 10.25/10.46 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 10.25/10.46 intro zenon_D_pnotp. % 10.25/10.46 apply zenon_H29e. % 10.25/10.46 rewrite <- zenon_D_pnotp. % 10.25/10.46 exact zenon_H79. % 10.25/10.46 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H297]. % 10.25/10.46 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.25/10.46 congruence. % 10.25/10.46 apply zenon_Hd7. apply refl_equal. % 10.25/10.46 apply zenon_H297. apply sym_equal. exact zenon_Ha5. % 10.25/10.46 apply zenon_Hd7. apply refl_equal. % 10.25/10.46 apply zenon_Hd7. apply refl_equal. % 10.25/10.46 (* end of lemma zenon_L579_ *) % 10.25/10.46 assert (zenon_L580_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H2cf zenon_H29d zenon_Ha5 zenon_H1e5 zenon_H1ee zenon_H1eb zenon_H2cd. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2cf); [ zenon_intro zenon_H79 | zenon_intro zenon_H2d0 ]. % 10.25/10.46 apply (zenon_L579_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2d0); [ zenon_intro zenon_H189 | zenon_intro zenon_H2d1 ]. % 10.25/10.46 exact (zenon_H1e5 zenon_H189). % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H67 ]. % 10.25/10.46 exact (zenon_H1ee zenon_Hd3). % 10.25/10.46 apply (zenon_L523_); trivial. % 10.25/10.46 (* end of lemma zenon_L580_ *) % 10.25/10.46 assert (zenon_L581_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H2cf zenon_Hd5 zenon_Hc7 zenon_H1e5 zenon_H1ee zenon_H158 zenon_He6. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2cf); [ zenon_intro zenon_H79 | zenon_intro zenon_H2d0 ]. % 10.25/10.46 apply (zenon_L506_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2d0); [ zenon_intro zenon_H189 | zenon_intro zenon_H2d1 ]. % 10.25/10.46 exact (zenon_H1e5 zenon_H189). % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H67 ]. % 10.25/10.46 exact (zenon_H1ee zenon_Hd3). % 10.25/10.46 apply (zenon_L186_); trivial. % 10.25/10.46 (* end of lemma zenon_L581_ *) % 10.25/10.46 assert (zenon_L582_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H269 zenon_H157 zenon_H284 zenon_H16e zenon_Hdd zenon_H24b zenon_H2cf zenon_Hd5 zenon_Hc7 zenon_H1e5 zenon_H1ee zenon_He6. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H56 | zenon_intro zenon_H26a ]. % 10.25/10.46 apply (zenon_L209_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H198 | zenon_intro zenon_H26b ]. % 10.25/10.46 apply (zenon_L258_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_He5 | zenon_intro zenon_H158 ]. % 10.25/10.46 apply (zenon_L213_); trivial. % 10.25/10.46 apply (zenon_L581_); trivial. % 10.25/10.46 (* end of lemma zenon_L582_ *) % 10.25/10.46 assert (zenon_L583_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H272 zenon_H2cd zenon_H1eb zenon_H29d zenon_He6 zenon_H1ee zenon_H1e5 zenon_Hd5 zenon_H2cf zenon_H24b zenon_Hdd zenon_H16e zenon_H284 zenon_H157 zenon_H269 zenon_H2f2 zenon_H2ed zenon_H262 zenon_H154 zenon_H202 zenon_H171 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H99 zenon_H1de zenon_H2d zenon_Hc3 zenon_H2ef zenon_H36 zenon_Hf4. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.46 apply (zenon_L496_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.46 apply (zenon_L580_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.46 apply (zenon_L582_); trivial. % 10.25/10.46 apply (zenon_L533_); trivial. % 10.25/10.46 (* end of lemma zenon_L583_ *) % 10.25/10.46 assert (zenon_L584_ : ((op (e3) (e3)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H79 zenon_H56 zenon_He6. % 10.25/10.46 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.25/10.46 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 10.25/10.46 intro zenon_D_pnotp. % 10.25/10.46 apply zenon_He6. % 10.25/10.46 rewrite <- zenon_D_pnotp. % 10.25/10.46 exact zenon_Hd6. % 10.25/10.46 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.25/10.46 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 10.25/10.46 congruence. % 10.25/10.46 cut (((op (e3) (e3)) = (e0)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 10.25/10.46 intro zenon_D_pnotp. % 10.25/10.46 apply zenon_He7. % 10.25/10.46 rewrite <- zenon_D_pnotp. % 10.25/10.46 exact zenon_H79. % 10.25/10.46 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H300]. % 10.25/10.46 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.25/10.46 congruence. % 10.25/10.46 apply zenon_Hd7. apply refl_equal. % 10.25/10.46 apply zenon_H300. apply sym_equal. exact zenon_H56. % 10.25/10.46 apply zenon_Hd7. apply refl_equal. % 10.25/10.46 apply zenon_Hd7. apply refl_equal. % 10.25/10.46 (* end of lemma zenon_L584_ *) % 10.25/10.46 assert (zenon_L585_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.25/10.46 do 0 intro. intros zenon_H293 zenon_H284 zenon_H198 zenon_H9a zenon_H99 zenon_Hf4 zenon_H51 zenon_H104 zenon_H1ed. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.25/10.46 apply (zenon_L258_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.25/10.46 apply (zenon_L35_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.25/10.46 apply (zenon_L328_); trivial. % 10.25/10.46 apply (zenon_L219_); trivial. % 10.25/10.46 (* end of lemma zenon_L585_ *) % 10.25/10.46 assert (zenon_L586_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 10.25/10.46 do 0 intro. intros zenon_H269 zenon_He6 zenon_H79 zenon_H1ed zenon_H104 zenon_H51 zenon_Hf4 zenon_H99 zenon_H9a zenon_H284 zenon_H293 zenon_Hdd zenon_H24b zenon_H17c. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H56 | zenon_intro zenon_H26a ]. % 10.25/10.46 apply (zenon_L584_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H198 | zenon_intro zenon_H26b ]. % 10.25/10.46 apply (zenon_L585_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_He5 | zenon_intro zenon_H158 ]. % 10.25/10.46 apply (zenon_L213_); trivial. % 10.25/10.46 apply (zenon_L253_); trivial. % 10.25/10.46 (* end of lemma zenon_L586_ *) % 10.25/10.46 assert (zenon_L587_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 10.25/10.46 do 0 intro. intros zenon_H245 zenon_H26e zenon_H2cd zenon_H1eb zenon_H1ee zenon_H1e5 zenon_H2ed zenon_H2cf zenon_He9 zenon_H269 zenon_He6 zenon_H1ed zenon_H104 zenon_H51 zenon_Hf4 zenon_H99 zenon_H9a zenon_H284 zenon_H293 zenon_Hdd zenon_H24b zenon_H17c. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.46 apply (zenon_L524_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.46 apply (zenon_L526_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.46 apply (zenon_L185_); trivial. % 10.25/10.46 apply (zenon_L586_); trivial. % 10.25/10.46 (* end of lemma zenon_L587_ *) % 10.25/10.46 assert (zenon_L588_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.46 do 0 intro. intros zenon_He0 zenon_Hfa zenon_H36 zenon_H2ef zenon_H2d zenon_H1de zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H171 zenon_H202 zenon_H154 zenon_H262 zenon_H2f2 zenon_H157 zenon_Hd5 zenon_H29d zenon_H272 zenon_H24b zenon_Hdd zenon_H293 zenon_H9a zenon_H99 zenon_H1ed zenon_He6 zenon_H269 zenon_He9 zenon_H2cf zenon_H2ed zenon_H1ee zenon_H1eb zenon_H2cd zenon_H26e zenon_H245 zenon_H298 zenon_H284 zenon_H16e zenon_H104 zenon_H17c zenon_Hf4 zenon_H1e5. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.46 apply (zenon_L59_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.46 apply (zenon_L583_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.46 apply (zenon_L587_); trivial. % 10.25/10.46 apply (zenon_L551_); trivial. % 10.25/10.46 (* end of lemma zenon_L588_ *) % 10.25/10.46 assert (zenon_L589_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 10.25/10.46 do 0 intro. intros zenon_H287 zenon_Hc1 zenon_H74. % 10.25/10.46 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 10.25/10.46 intro zenon_D_pnotp. % 10.25/10.46 apply zenon_H287. % 10.25/10.46 rewrite <- zenon_D_pnotp. % 10.25/10.46 exact zenon_Hc1. % 10.25/10.46 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H301]. % 10.25/10.46 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 10.25/10.46 congruence. % 10.25/10.46 apply zenon_Hbd. apply refl_equal. % 10.25/10.46 apply zenon_H301. apply sym_equal. exact zenon_H74. % 10.25/10.46 (* end of lemma zenon_L589_ *) % 10.25/10.46 assert (zenon_L590_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 10.25/10.46 do 0 intro. intros zenon_H245 zenon_H133 zenon_H2cd zenon_H1eb zenon_H1ee zenon_H1e5 zenon_H2ed zenon_H2cf zenon_He9 zenon_H269 zenon_He6 zenon_H1ed zenon_H104 zenon_H51 zenon_Hf4 zenon_H99 zenon_H9a zenon_H284 zenon_H293 zenon_Hdd zenon_H24b zenon_H17c. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.46 apply (zenon_L110_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.46 apply (zenon_L526_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.46 apply (zenon_L185_); trivial. % 10.25/10.46 apply (zenon_L586_); trivial. % 10.25/10.46 (* end of lemma zenon_L590_ *) % 10.25/10.46 assert (zenon_L591_ : (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e0)) = (e0)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> False). % 10.25/10.46 do 0 intro. intros zenon_Hc6 zenon_Hdd zenon_H133 zenon_H1eb zenon_H1ee zenon_H1e5 zenon_H269 zenon_He6 zenon_H1ed zenon_H9a zenon_H284 zenon_H293 zenon_H24b zenon_H17c zenon_Hc1 zenon_He0 zenon_H2b9 zenon_H85 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_Hf4 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_H104 zenon_He9 zenon_H99 zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H36 zenon_H2e7 zenon_H2e4 zenon_H2d zenon_H171 zenon_H2f5 zenon_Hfd. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.25/10.46 apply (zenon_L134_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.25/10.46 apply (zenon_L225_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.46 apply (zenon_L417_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.46 apply (zenon_L73_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.46 apply (zenon_L590_); trivial. % 10.25/10.46 apply (zenon_L238_); trivial. % 10.25/10.46 apply (zenon_L545_); trivial. % 10.25/10.46 (* end of lemma zenon_L591_ *) % 10.25/10.46 assert (zenon_L592_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> False). % 10.25/10.46 do 0 intro. intros zenon_H17e zenon_H46 zenon_H16e zenon_H104 zenon_H36 zenon_H186 zenon_H1ed zenon_H24b zenon_H158. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.46 apply (zenon_L556_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.46 apply (zenon_L225_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.46 apply (zenon_L249_); trivial. % 10.25/10.46 apply (zenon_L253_); trivial. % 10.25/10.46 (* end of lemma zenon_L592_ *) % 10.25/10.46 assert (zenon_L593_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H191 zenon_H157 zenon_Hd5 zenon_H29d zenon_H272 zenon_H15e zenon_H287 zenon_Hc1 zenon_Hc6 zenon_H1eb zenon_H1ee zenon_H1e5 zenon_H269 zenon_He6 zenon_H284 zenon_H293 zenon_He0 zenon_H2b9 zenon_H85 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_Hf4 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_H99 zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H171 zenon_H2f5 zenon_Hfd zenon_H45 zenon_H2ae zenon_H94 zenon_H182 zenon_H298 zenon_Hdf zenon_He9 zenon_H2d zenon_H17e zenon_H46 zenon_H16e zenon_H104 zenon_H36 zenon_H186 zenon_H1ed zenon_H24b. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.25/10.46 apply (zenon_L57_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.25/10.46 apply (zenon_L282_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.25/10.46 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.46 apply (zenon_L511_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.46 apply (zenon_L310_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.46 apply (zenon_L578_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.46 apply (zenon_L556_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.46 apply (zenon_L225_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.46 apply (zenon_L249_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.25/10.46 exact (zenon_H45 zenon_H42). % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.25/10.46 apply (zenon_L588_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.25/10.46 apply (zenon_L589_); trivial. % 10.25/10.46 apply (zenon_L185_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.46 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.46 apply (zenon_L511_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.46 apply (zenon_L310_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.46 apply (zenon_L578_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.46 apply (zenon_L359_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.46 apply (zenon_L225_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.46 apply (zenon_L249_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.25/10.46 exact (zenon_H45 zenon_H42). % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.25/10.46 apply (zenon_L591_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.25/10.46 apply (zenon_L589_); trivial. % 10.25/10.46 apply (zenon_L185_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.46 apply (zenon_L134_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.46 apply (zenon_L565_); trivial. % 10.25/10.46 apply (zenon_L592_); trivial. % 10.25/10.46 (* end of lemma zenon_L593_ *) % 10.25/10.46 assert (zenon_L594_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.46 do 0 intro. intros zenon_He0 zenon_Hc0 zenon_H46 zenon_Hc4 zenon_H85 zenon_H24b zenon_Hdd zenon_H293 zenon_H9a zenon_H99 zenon_H1ed zenon_He6 zenon_H269 zenon_He9 zenon_H2cf zenon_H2ed zenon_H1ee zenon_H1eb zenon_H2cd zenon_H26e zenon_H245 zenon_H298 zenon_H284 zenon_H16e zenon_H104 zenon_H17c zenon_Hf4 zenon_H1e5. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.46 apply (zenon_L88_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.46 apply (zenon_L45_); trivial. % 10.25/10.46 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.46 apply (zenon_L587_); trivial. % 10.25/10.46 apply (zenon_L551_); trivial. % 10.25/10.46 (* end of lemma zenon_L594_ *) % 10.25/10.46 assert (zenon_L595_ : ((op (e2) (e2)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.25/10.46 do 0 intro. intros zenon_H74 zenon_H51 zenon_H85. % 10.25/10.46 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.25/10.46 cut (((e2) = (e2)) = ((e0) = (e2))). % 10.25/10.46 intro zenon_D_pnotp. % 10.25/10.46 apply zenon_H85. % 10.25/10.46 rewrite <- zenon_D_pnotp. % 10.25/10.46 exact zenon_H86. % 10.25/10.46 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.25/10.46 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 10.25/10.46 congruence. % 10.25/10.46 cut (((op (e2) (e2)) = (e0)) = ((e2) = (e0))). % 10.25/10.46 intro zenon_D_pnotp. % 10.25/10.46 apply zenon_H88. % 10.25/10.46 rewrite <- zenon_D_pnotp. % 10.25/10.46 exact zenon_H74. % 10.25/10.46 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.46 cut (((op (e2) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 10.25/10.46 congruence. % 10.25/10.46 exact (zenon_H50 zenon_H51). % 10.25/10.46 apply zenon_H84. apply refl_equal. % 10.25/10.46 apply zenon_H87. apply refl_equal. % 10.25/10.46 apply zenon_H87. apply refl_equal. % 10.25/10.46 (* end of lemma zenon_L595_ *) % 10.25/10.46 assert (zenon_L596_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.47 do 0 intro. intros zenon_He0 zenon_Hc0 zenon_H46 zenon_H36 zenon_H2ef zenon_H2d zenon_H1de zenon_H99 zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H171 zenon_H202 zenon_H154 zenon_H262 zenon_H2ed zenon_H2f2 zenon_He9 zenon_H2cf zenon_H1eb zenon_H2cd zenon_H26e zenon_H245 zenon_H85 zenon_H74 zenon_H298 zenon_H284 zenon_H16e zenon_H104 zenon_H17c zenon_Hf4 zenon_H1e5. % 10.25/10.47 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.47 apply (zenon_L88_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.47 apply (zenon_L535_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.47 apply (zenon_L595_); trivial. % 10.25/10.47 apply (zenon_L551_); trivial. % 10.25/10.47 (* end of lemma zenon_L596_ *) % 10.25/10.47 assert (zenon_L597_ : ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((e0) = (e3))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.47 do 0 intro. intros zenon_H5a zenon_Hca zenon_H186 zenon_H17e zenon_Hdf zenon_H182 zenon_H94 zenon_Hfd zenon_H2f5 zenon_H12a zenon_H2b9 zenon_Hc6 zenon_H287 zenon_H15e zenon_H272 zenon_H29d zenon_H191 zenon_H1ed zenon_H293 zenon_H45 zenon_H2ae zenon_Hf4 zenon_H104 zenon_H298 zenon_H85 zenon_H245 zenon_H26e zenon_H2cd zenon_H1eb zenon_He9 zenon_H2f2 zenon_H2ed zenon_H262 zenon_H154 zenon_H202 zenon_H171 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H99 zenon_H1de zenon_H2d zenon_H2ef zenon_H36 zenon_H46 zenon_Hc0 zenon_He0 zenon_H269 zenon_H157 zenon_H284 zenon_H16e zenon_H24b zenon_H2cf zenon_Hd5 zenon_H1e5 zenon_H1ee zenon_He6. % 10.25/10.47 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.47 apply (zenon_L511_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.47 apply (zenon_L310_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.47 apply (zenon_L359_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.47 apply (zenon_L225_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.47 apply (zenon_L249_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.47 apply (zenon_L88_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.47 apply (zenon_L535_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.47 apply (zenon_L307_); trivial. % 10.25/10.47 apply (zenon_L551_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.25/10.47 apply (zenon_L556_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.25/10.47 apply (zenon_L225_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.25/10.47 apply (zenon_L249_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.25/10.47 apply (zenon_L593_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.25/10.47 exact (zenon_H45 zenon_H42). % 10.25/10.47 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.25/10.47 apply (zenon_L594_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.25/10.47 apply (zenon_L596_); trivial. % 10.25/10.47 apply (zenon_L185_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.25/10.47 apply (zenon_L596_); trivial. % 10.25/10.47 apply (zenon_L582_); trivial. % 10.25/10.47 (* end of lemma zenon_L597_ *) % 10.25/10.47 assert (zenon_L598_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.25/10.47 do 0 intro. intros zenon_H293 zenon_H284 zenon_H198 zenon_H9a zenon_H99 zenon_H163 zenon_H104 zenon_H1ed. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.25/10.47 apply (zenon_L258_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.25/10.47 apply (zenon_L35_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.25/10.47 exact (zenon_H163 zenon_H103). % 10.25/10.47 apply (zenon_L219_); trivial. % 10.25/10.47 (* end of lemma zenon_L598_ *) % 10.25/10.47 assert (zenon_L599_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.25/10.47 do 0 intro. intros zenon_H293 zenon_H284 zenon_H198 zenon_H9c zenon_H36 zenon_H99 zenon_H74 zenon_H104 zenon_H1ed. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.25/10.47 apply (zenon_L258_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.25/10.47 apply (zenon_L36_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.25/10.47 apply (zenon_L442_); trivial. % 10.25/10.47 apply (zenon_L219_); trivial. % 10.25/10.47 (* end of lemma zenon_L599_ *) % 10.25/10.47 assert (zenon_L600_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.25/10.47 do 0 intro. intros zenon_H2ae zenon_H45 zenon_H163 zenon_H104 zenon_H99 zenon_H36 zenon_H9c zenon_H198 zenon_H284 zenon_H293 zenon_He9 zenon_H1ed. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.25/10.47 exact (zenon_H45 zenon_H42). % 10.25/10.47 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.25/10.47 apply (zenon_L598_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.25/10.47 apply (zenon_L599_); trivial. % 10.25/10.47 apply (zenon_L185_); trivial. % 10.25/10.47 (* end of lemma zenon_L600_ *) % 10.25/10.47 assert (zenon_L601_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.25/10.47 do 0 intro. intros zenon_H1a2 zenon_H24b zenon_H186 zenon_H46 zenon_H17e zenon_H27c zenon_H2d zenon_Hca zenon_Hdf zenon_H182 zenon_H94 zenon_Hfd zenon_H2f5 zenon_H12a zenon_H2b9 zenon_Hc6 zenon_H287 zenon_H15e zenon_H272 zenon_H29d zenon_H191 zenon_Hf4 zenon_H298 zenon_H85 zenon_H245 zenon_H26e zenon_H2cd zenon_H1eb zenon_H2f2 zenon_H2ed zenon_H262 zenon_H154 zenon_H202 zenon_H171 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H1de zenon_H2ef zenon_Hc0 zenon_He0 zenon_H269 zenon_H157 zenon_H2cf zenon_Hd5 zenon_H1e5 zenon_H1ee zenon_He6 zenon_H2ae zenon_H45 zenon_H163 zenon_H104 zenon_H99 zenon_H36 zenon_H9c zenon_H284 zenon_H293 zenon_He9 zenon_H1ed. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.25/10.47 apply (zenon_L57_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.25/10.47 apply (zenon_L58_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.47 apply (zenon_L597_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.47 apply (zenon_L134_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.47 apply (zenon_L252_); trivial. % 10.25/10.47 apply (zenon_L592_); trivial. % 10.25/10.47 apply (zenon_L600_); trivial. % 10.25/10.47 (* end of lemma zenon_L601_ *) % 10.25/10.47 assert (zenon_L602_ : (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.25/10.47 do 0 intro. intros zenon_H100 zenon_Hda zenon_H2bc zenon_H244 zenon_H130 zenon_H2a8 zenon_H1a3 zenon_H124 zenon_H278 zenon_H14b zenon_He9 zenon_H293 zenon_H284 zenon_H9c zenon_H99 zenon_H104 zenon_H163 zenon_H2ae zenon_He6 zenon_H1e5 zenon_Hd5 zenon_H2cf zenon_H157 zenon_H269 zenon_He0 zenon_Hc0 zenon_H2ef zenon_H1de zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H171 zenon_H202 zenon_H154 zenon_H262 zenon_H2ed zenon_H2f2 zenon_H2cd zenon_H26e zenon_H245 zenon_H85 zenon_H298 zenon_H191 zenon_H29d zenon_H272 zenon_H15e zenon_H287 zenon_Hc6 zenon_H2b9 zenon_H12a zenon_H2f5 zenon_Hfd zenon_H94 zenon_H182 zenon_Hdf zenon_Hca zenon_H2d zenon_H27c zenon_H17e zenon_H186 zenon_H24b zenon_H1a2 zenon_H36 zenon_Hf4. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.25/10.47 apply (zenon_L1_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.25/10.47 apply (zenon_L2_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.25/10.47 apply (zenon_L3_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.25/10.47 apply (zenon_L4_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.25/10.47 apply (zenon_L5_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.25/10.47 apply (zenon_L6_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.25/10.47 apply (zenon_L491_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.25/10.47 apply (zenon_L492_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.25/10.47 apply (zenon_L10_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.25/10.47 apply (zenon_L493_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.25/10.47 apply (zenon_L13_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.25/10.47 apply (zenon_L495_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.25/10.47 apply (zenon_L15_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.25/10.47 apply (zenon_L497_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.25/10.47 apply (zenon_L498_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.25/10.47 apply (zenon_L19_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.25/10.47 apply (zenon_L20_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.25/10.47 apply (zenon_L21_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.25/10.47 apply (zenon_L499_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.25/10.47 apply (zenon_L500_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.25/10.47 apply (zenon_L24_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.25/10.47 apply (zenon_L25_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.25/10.47 apply (zenon_L26_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.25/10.47 apply (zenon_L27_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.25/10.47 apply (zenon_L501_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.25/10.47 apply (zenon_L31_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.25/10.47 apply (zenon_L32_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.25/10.47 apply (zenon_L502_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.25/10.47 apply (zenon_L503_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.25/10.47 apply (zenon_L56_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.25/10.47 apply (zenon_L106_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.25/10.47 apply (zenon_L147_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.25/10.47 apply (zenon_L148_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.25/10.47 apply (zenon_L505_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.25/10.47 apply (zenon_L150_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.25/10.47 apply (zenon_L508_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.25/10.47 apply (zenon_L509_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.25/10.47 apply (zenon_L154_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.25/10.47 apply (zenon_L155_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.25/10.47 apply (zenon_L510_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.25/10.47 apply (zenon_L157_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.25/10.47 apply (zenon_L158_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.25/10.47 apply (zenon_L159_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.25/10.47 apply (zenon_L160_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.25/10.47 apply (zenon_L574_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.25/10.47 apply (zenon_L292_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.25/10.47 apply (zenon_L164_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.25/10.47 apply (zenon_L165_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.25/10.47 apply (zenon_L166_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.25/10.47 apply (zenon_L518_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.25/10.47 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_H13b. zenon_intro zenon_H1db. % 10.25/10.47 apply (zenon_and_s _ _ zenon_H1db). zenon_intro zenon_H76. zenon_intro zenon_H27. % 10.25/10.47 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.25/10.47 apply (zenon_L576_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.25/10.47 apply (zenon_L169_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.25/10.47 apply (zenon_L520_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.25/10.47 apply (zenon_L172_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.25/10.47 apply (zenon_L577_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.25/10.47 apply (zenon_L174_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.25/10.47 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ed. zenon_intro zenon_H1ec. % 10.25/10.47 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ee. zenon_intro zenon_H43. % 10.25/10.47 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.25/10.47 apply (zenon_L601_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.25/10.47 apply (zenon_L369_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.25/10.47 apply (zenon_L178_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.25/10.47 apply (zenon_L179_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.25/10.47 apply (zenon_L180_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.25/10.47 apply (zenon_L181_); trivial. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.25/10.47 apply (zenon_L182_); trivial. % 10.25/10.47 apply (zenon_L183_); trivial. % 10.25/10.47 (* end of lemma zenon_L602_ *) % 10.25/10.47 assert (zenon_L603_ : (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> False). % 10.25/10.47 do 0 intro. intros zenon_H163 zenon_H36 zenon_Hf4 zenon_H2d zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H85 zenon_H100 zenon_Hd5 zenon_Hca zenon_H104 zenon_H99 zenon_H14b zenon_H191 zenon_H287 zenon_H124 zenon_H157 zenon_He9 zenon_H298 zenon_Hc0 zenon_H182 zenon_He0 zenon_Hdf zenon_Hc6 zenon_H2f5 zenon_H171 zenon_H1b2 zenon_H2ea zenon_Hfd zenon_H1de zenon_H12a zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H17e zenon_H2a8 zenon_H130 zenon_H27c zenon_H29d zenon_H244 zenon_H293 zenon_H284 zenon_Hda zenon_H2bc zenon_H2b9 zenon_H1a3 zenon_H94 zenon_H272 zenon_H186 zenon_H1a2 zenon_H278 zenon_H15e zenon_H269 zenon_He6 zenon_H24b zenon_H2ae. % 10.25/10.47 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H127 ]. % 10.25/10.47 apply (zenon_L602_); trivial. % 10.25/10.47 apply (zenon_L545_); trivial. % 10.25/10.47 (* end of lemma zenon_L603_ *) % 10.25/10.47 assert (zenon_L604_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> False). % 10.25/10.48 do 0 intro. intros zenon_H302 zenon_H2ae zenon_H24b zenon_He6 zenon_H269 zenon_H15e zenon_H278 zenon_H1a2 zenon_H186 zenon_H272 zenon_H94 zenon_H1a3 zenon_H2b9 zenon_H2bc zenon_Hda zenon_H284 zenon_H293 zenon_H244 zenon_H29d zenon_H27c zenon_H130 zenon_H2a8 zenon_H17e zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_Hfd zenon_H2ea zenon_H1b2 zenon_H171 zenon_H2f5 zenon_Hc6 zenon_Hdf zenon_He0 zenon_H182 zenon_Hc0 zenon_H298 zenon_He9 zenon_H157 zenon_H124 zenon_H287 zenon_H191 zenon_H14b zenon_H99 zenon_H104 zenon_Hca zenon_Hd5 zenon_H100 zenon_H85 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H2d zenon_Hf4 zenon_H36. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H163 | zenon_intro zenon_Hc3 ]. % 10.25/10.48 apply (zenon_L603_); trivial. % 10.25/10.48 apply (zenon_L536_); trivial. % 10.25/10.48 (* end of lemma zenon_L604_ *) % 10.25/10.48 assert (zenon_L605_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> False). % 10.25/10.48 do 0 intro. intros zenon_H12d zenon_H99 zenon_H85 zenon_H12a zenon_Hf6 zenon_H104 zenon_H36 zenon_Hfd zenon_Hc3 zenon_He9. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.48 apply (zenon_L58_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.48 apply (zenon_L312_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.48 apply (zenon_L45_); trivial. % 10.25/10.48 apply (zenon_L279_); trivial. % 10.25/10.48 (* end of lemma zenon_L605_ *) % 10.25/10.48 assert (zenon_L606_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.48 do 0 intro. intros zenon_H12d zenon_Hfd zenon_H2f5 zenon_H171 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H104 zenon_H1de zenon_H12a zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_Hf4 zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_H99 zenon_H36 zenon_Hc3 zenon_H85 zenon_He9 zenon_H127. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.48 apply (zenon_L545_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.48 apply (zenon_L312_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.48 apply (zenon_L45_); trivial. % 10.25/10.48 apply (zenon_L77_); trivial. % 10.25/10.48 (* end of lemma zenon_L606_ *) % 10.25/10.48 assert (zenon_L607_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.25/10.48 do 0 intro. intros zenon_H52 zenon_Hfd zenon_H67. % 10.25/10.48 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H42. zenon_intro zenon_H53. % 10.25/10.48 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H44. zenon_intro zenon_H1c8. % 10.25/10.48 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.25/10.48 apply (zenon_L353_); trivial. % 10.25/10.48 (* end of lemma zenon_L607_ *) % 10.25/10.48 assert (zenon_L608_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (~((e2) = (e3))) -> False). % 10.25/10.48 do 0 intro. intros zenon_H244 zenon_H13d zenon_H13c zenon_He9 zenon_H85 zenon_Hc3 zenon_H36 zenon_H99 zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_Hf4 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_H104 zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H171 zenon_H2f5 zenon_H12d zenon_H1f9 zenon_H52 zenon_Hfd. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.25/10.48 apply (zenon_L85_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.25/10.48 apply (zenon_L606_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.25/10.48 exact (zenon_H1f9 zenon_H1ed). % 10.25/10.48 apply (zenon_L607_); trivial. % 10.25/10.48 (* end of lemma zenon_L608_ *) % 10.25/10.48 assert (zenon_L609_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.25/10.48 do 0 intro. intros zenon_H303 zenon_H47 zenon_H42 zenon_H2f zenon_H44 zenon_H13b zenon_H130. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H1f | zenon_intro zenon_H304 ]. % 10.25/10.48 apply (zenon_L11_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H31 | zenon_intro zenon_H305 ]. % 10.25/10.48 exact (zenon_H2f zenon_H31). % 10.25/10.48 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H46 | zenon_intro zenon_H5a ]. % 10.25/10.48 exact (zenon_H44 zenon_H46). % 10.25/10.48 apply (zenon_L133_); trivial. % 10.25/10.48 (* end of lemma zenon_L609_ *) % 10.25/10.48 assert (zenon_L610_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.25/10.48 do 0 intro. intros zenon_H244 zenon_H136 zenon_H128 zenon_He9 zenon_H1f9 zenon_Hfd zenon_Hd3. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.25/10.48 apply (zenon_L255_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.25/10.48 apply (zenon_L77_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.25/10.48 exact (zenon_H1f9 zenon_H1ed). % 10.25/10.48 apply (zenon_L353_); trivial. % 10.25/10.48 (* end of lemma zenon_L610_ *) % 10.25/10.48 assert (zenon_L611_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.25/10.48 do 0 intro. intros zenon_H12d zenon_H2e4 zenon_H42 zenon_H99 zenon_H36 zenon_Hc3 zenon_H85 zenon_H244 zenon_H136 zenon_He9 zenon_H1f9 zenon_Hfd zenon_Hd3. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.48 apply (zenon_L494_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.48 apply (zenon_L312_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.48 apply (zenon_L45_); trivial. % 10.25/10.48 apply (zenon_L610_); trivial. % 10.25/10.48 (* end of lemma zenon_L611_ *) % 10.25/10.48 assert (zenon_L612_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.25/10.48 do 0 intro. intros zenon_H281 zenon_H104 zenon_H198 zenon_Hcd zenon_H289 zenon_H52 zenon_H2f5 zenon_H171 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H1de zenon_H12a zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_H13d zenon_H14b zenon_H135 zenon_H303 zenon_H47 zenon_H2f zenon_H44 zenon_H130 zenon_H15e zenon_Hfa zenon_Hf4 zenon_H12d zenon_H2e4 zenon_H42 zenon_H99 zenon_H36 zenon_Hc3 zenon_H85 zenon_H244 zenon_He9 zenon_H1f9 zenon_Hfd zenon_Hd3. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.48 exact (zenon_H44 zenon_H46). % 10.25/10.48 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.48 apply (zenon_L541_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.25/10.48 apply (zenon_L541_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.25/10.48 apply (zenon_L608_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.25/10.48 apply (zenon_L354_); trivial. % 10.25/10.48 apply (zenon_L609_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.48 apply (zenon_L91_); trivial. % 10.25/10.48 apply (zenon_L135_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.48 apply (zenon_L59_); trivial. % 10.25/10.48 apply (zenon_L611_); trivial. % 10.25/10.48 (* end of lemma zenon_L612_ *) % 10.25/10.48 assert (zenon_L613_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.25/10.48 do 0 intro. intros zenon_H1a3 zenon_H100 zenon_Hd3 zenon_Hfd zenon_H1f9 zenon_He9 zenon_H244 zenon_H85 zenon_Hc3 zenon_H36 zenon_H99 zenon_H42 zenon_H2e4 zenon_H12d zenon_Hfa zenon_H15e zenon_H130 zenon_H44 zenon_H2f zenon_H47 zenon_H303 zenon_H135 zenon_H14b zenon_H13d zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H171 zenon_H2f5 zenon_H52 zenon_H289 zenon_H104 zenon_H281 zenon_H198 zenon_Hf4. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.48 exact (zenon_H44 zenon_H46). % 10.25/10.48 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.48 apply (zenon_L281_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.48 apply (zenon_L612_); trivial. % 10.25/10.48 apply (zenon_L143_); trivial. % 10.25/10.48 (* end of lemma zenon_L613_ *) % 10.25/10.48 assert (zenon_L614_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (~((e2) = (e3))) -> False). % 10.25/10.48 do 0 intro. intros zenon_H244 zenon_H133 zenon_H104 zenon_H128 zenon_He9 zenon_H1f9 zenon_H52 zenon_Hfd. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.25/10.48 apply (zenon_L123_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.25/10.48 apply (zenon_L77_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.25/10.48 exact (zenon_H1f9 zenon_H1ed). % 10.25/10.48 apply (zenon_L607_); trivial. % 10.25/10.48 (* end of lemma zenon_L614_ *) % 10.25/10.48 assert (zenon_L615_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (~((e2) = (e3))) -> False). % 10.25/10.48 do 0 intro. intros zenon_H12d zenon_H119 zenon_H99 zenon_H36 zenon_Hc3 zenon_H85 zenon_H244 zenon_H133 zenon_H104 zenon_He9 zenon_H1f9 zenon_H52 zenon_Hfd. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.48 apply (zenon_L134_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.48 apply (zenon_L312_); trivial. % 10.25/10.48 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.48 apply (zenon_L45_); trivial. % 10.25/10.48 apply (zenon_L614_); trivial. % 10.25/10.48 (* end of lemma zenon_L615_ *) % 10.25/10.48 assert (zenon_L616_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.25/10.48 do 0 intro. intros zenon_H42 zenon_H150 zenon_He9. % 10.25/10.48 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.25/10.48 cut (((e3) = (e3)) = ((e0) = (e3))). % 10.25/10.48 intro zenon_D_pnotp. % 10.25/10.48 apply zenon_He9. % 10.25/10.48 rewrite <- zenon_D_pnotp. % 10.25/10.48 exact zenon_Hea. % 10.25/10.48 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.25/10.48 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 10.25/10.48 congruence. % 10.25/10.48 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 10.25/10.48 intro zenon_D_pnotp. % 10.25/10.48 apply zenon_Hec. % 10.25/10.48 rewrite <- zenon_D_pnotp. % 10.25/10.48 exact zenon_H42. % 10.25/10.48 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.48 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 10.25/10.48 congruence. % 10.25/10.48 exact (zenon_H151 zenon_H150). % 10.25/10.48 apply zenon_H84. apply refl_equal. % 10.25/10.48 apply zenon_Heb. apply refl_equal. % 10.25/10.48 apply zenon_Heb. apply refl_equal. % 10.25/10.48 (* end of lemma zenon_L616_ *) % 10.25/10.48 assert (zenon_L617_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (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)) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H191 zenon_H95 zenon_Hf4 zenon_H289 zenon_H2f5 zenon_H171 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H2ea zenon_H1de zenon_H12a zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_H13d zenon_H14b zenon_H135 zenon_H303 zenon_H47 zenon_H2f zenon_H130 zenon_H100 zenon_H1a3 zenon_H281 zenon_H44 zenon_H104 zenon_H198 zenon_H52 zenon_H15e zenon_H1b2 zenon_H12d zenon_H2e4 zenon_H42 zenon_H99 zenon_H36 zenon_Hc3 zenon_H85 zenon_H244 zenon_He9 zenon_H1f9 zenon_Hfd zenon_Hd3. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.25/10.49 exact (zenon_H2f zenon_H31). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.25/10.49 apply (zenon_L394_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.25/10.49 apply (zenon_L613_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.49 exact (zenon_H44 zenon_H46). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.49 apply (zenon_L541_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.49 apply (zenon_L615_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.49 apply (zenon_L616_); trivial. % 10.25/10.49 apply (zenon_L135_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.49 apply (zenon_L152_); trivial. % 10.25/10.49 apply (zenon_L611_); trivial. % 10.25/10.49 (* end of lemma zenon_L617_ *) % 10.25/10.49 assert (zenon_L618_ : (((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 (e1) (e0)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (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)) = (e2))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H1a2 zenon_H191 zenon_H95 zenon_Hf4 zenon_H289 zenon_H2f5 zenon_H171 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H2ea zenon_H1de zenon_H12a zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_H13d zenon_H14b zenon_H135 zenon_H303 zenon_H47 zenon_H2f zenon_H130 zenon_H100 zenon_H1a3 zenon_H281 zenon_H44 zenon_H104 zenon_H52 zenon_H15e zenon_H1b2 zenon_H12d zenon_H2e4 zenon_H42 zenon_H99 zenon_H36 zenon_Hc3 zenon_H85 zenon_H244 zenon_He9 zenon_H1f9 zenon_Hfd zenon_Hd3. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.25/10.49 exact (zenon_H2f zenon_H31). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.25/10.49 apply (zenon_L605_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.25/10.49 apply (zenon_L421_); trivial. % 10.25/10.49 apply (zenon_L617_); trivial. % 10.25/10.49 (* end of lemma zenon_L618_ *) % 10.25/10.49 assert (zenon_L619_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H56 zenon_H42 zenon_H284. % 10.25/10.49 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H5c | zenon_intro zenon_H5d ]. % 10.25/10.49 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e2)) = (op (e0) (e3)))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_H284. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_H5c. % 10.25/10.49 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.25/10.49 cut (((op (e0) (e3)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H285]. % 10.25/10.49 congruence. % 10.25/10.49 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e0) (e2)))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_H285. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_H56. % 10.25/10.49 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H306]. % 10.25/10.49 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 10.25/10.49 congruence. % 10.25/10.49 apply zenon_H5d. apply refl_equal. % 10.25/10.49 apply zenon_H306. apply sym_equal. exact zenon_H42. % 10.25/10.49 apply zenon_H5d. apply refl_equal. % 10.25/10.49 apply zenon_H5d. apply refl_equal. % 10.25/10.49 (* end of lemma zenon_L619_ *) % 10.25/10.49 assert (zenon_L620_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H272 zenon_H284 zenon_H42 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_Hdf zenon_H36 zenon_Hcd zenon_Hda zenon_Hc6 zenon_H298 zenon_Hd4 zenon_H85 zenon_H244 zenon_H130 zenon_H5a zenon_H252 zenon_Hfd zenon_H186 zenon_H17a zenon_He9. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.49 apply (zenon_L619_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.49 apply (zenon_L547_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.49 apply (zenon_L234_); trivial. % 10.25/10.49 apply (zenon_L549_); trivial. % 10.25/10.49 (* end of lemma zenon_L620_ *) % 10.25/10.49 assert (zenon_L621_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_He0 zenon_Hbb zenon_Hba zenon_Hd3 zenon_H1f9 zenon_H2e4 zenon_H12d zenon_H1b2 zenon_H15e zenon_H52 zenon_H104 zenon_H44 zenon_H281 zenon_H1a3 zenon_H100 zenon_H2f zenon_H47 zenon_H303 zenon_H135 zenon_H14b zenon_H13d zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_H2ea zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H171 zenon_H2f5 zenon_H289 zenon_H95 zenon_H191 zenon_H1a2 zenon_Hce zenon_H272 zenon_H284 zenon_H42 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_Hdf zenon_H36 zenon_Hcd zenon_Hda zenon_Hc6 zenon_H298 zenon_H85 zenon_H244 zenon_H130 zenon_H5a zenon_H252 zenon_Hfd zenon_H186 zenon_H17a zenon_He9. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.49 apply (zenon_L43_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.49 apply (zenon_L618_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.49 apply (zenon_L48_); trivial. % 10.25/10.49 apply (zenon_L620_); trivial. % 10.25/10.49 (* end of lemma zenon_L621_ *) % 10.25/10.49 assert (zenon_L622_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.49 do 0 intro. intros zenon_He0 zenon_Hfa zenon_Hfd zenon_H120 zenon_Hce zenon_H298 zenon_Hc6 zenon_Hda zenon_Hcd zenon_H36 zenon_H5a zenon_Hdf zenon_Ha5 zenon_H99 zenon_Hf4 zenon_H1e5. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.49 apply (zenon_L59_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.49 apply (zenon_L73_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.49 apply (zenon_L48_); trivial. % 10.25/10.49 apply (zenon_L547_); trivial. % 10.25/10.49 (* end of lemma zenon_L622_ *) % 10.25/10.49 assert (zenon_L623_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H2b9 zenon_Hf6 zenon_H36 zenon_Hf4 zenon_Hc4 zenon_H85 zenon_Hfd zenon_H127. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.49 apply (zenon_L89_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.49 apply (zenon_L310_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.49 apply (zenon_L45_); trivial. % 10.25/10.49 apply (zenon_L199_); trivial. % 10.25/10.49 (* end of lemma zenon_L623_ *) % 10.25/10.49 assert (zenon_L624_ : ((op (e3) (e3)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H79 zenon_Hd3 zenon_H85. % 10.25/10.49 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.25/10.49 cut (((e2) = (e2)) = ((e0) = (e2))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_H85. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_H86. % 10.25/10.49 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.25/10.49 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 10.25/10.49 congruence. % 10.25/10.49 cut (((op (e3) (e3)) = (e0)) = ((e2) = (e0))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_H88. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_H79. % 10.25/10.49 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.49 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 10.25/10.49 congruence. % 10.25/10.49 exact (zenon_H1ee zenon_Hd3). % 10.25/10.49 apply zenon_H84. apply refl_equal. % 10.25/10.49 apply zenon_H87. apply refl_equal. % 10.25/10.49 apply zenon_H87. apply refl_equal. % 10.25/10.49 (* end of lemma zenon_L624_ *) % 10.25/10.49 assert (zenon_L625_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H272 zenon_He9 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_H158 zenon_H104 zenon_H298 zenon_Hd4 zenon_Hd3 zenon_H85. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.49 apply (zenon_L324_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.49 apply (zenon_L325_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.49 apply (zenon_L234_); trivial. % 10.25/10.49 apply (zenon_L624_); trivial. % 10.25/10.49 (* end of lemma zenon_L625_ *) % 10.25/10.49 assert (zenon_L626_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_He0 zenon_Hbb zenon_Hba zenon_Hfd zenon_H120 zenon_Hce zenon_Hcd zenon_H272 zenon_He9 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_H158 zenon_H104 zenon_H298 zenon_Hd3 zenon_H85. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.49 apply (zenon_L43_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.49 apply (zenon_L73_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.49 apply (zenon_L48_); trivial. % 10.25/10.49 apply (zenon_L625_); trivial. % 10.25/10.49 (* end of lemma zenon_L626_ *) % 10.25/10.49 assert (zenon_L627_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e1))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H12a zenon_Hd3 zenon_H298 zenon_H104 zenon_H158 zenon_H99 zenon_H1e5 zenon_He9 zenon_H272 zenon_Hcd zenon_Hce zenon_Hba zenon_Hbb zenon_He0 zenon_H2b9 zenon_Hf6 zenon_H36 zenon_Hf4 zenon_Hc4 zenon_H85 zenon_Hfd. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.25/10.49 apply (zenon_L99_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.25/10.49 apply (zenon_L225_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.25/10.49 apply (zenon_L626_); trivial. % 10.25/10.49 apply (zenon_L623_); trivial. % 10.25/10.49 (* end of lemma zenon_L627_ *) % 10.25/10.49 assert (zenon_L628_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H131 zenon_H136 zenon_H85. % 10.25/10.49 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.25/10.49 cut (((e2) = (e2)) = ((e0) = (e2))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_H85. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_H86. % 10.25/10.49 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.25/10.49 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 10.25/10.49 congruence. % 10.25/10.49 cut (((op (e3) (e0)) = (e0)) = ((e2) = (e0))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_H88. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_H131. % 10.25/10.49 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.49 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H280]. % 10.25/10.49 congruence. % 10.25/10.49 exact (zenon_H280 zenon_H136). % 10.25/10.49 apply zenon_H84. apply refl_equal. % 10.25/10.49 apply zenon_H87. apply refl_equal. % 10.25/10.49 apply zenon_H87. apply refl_equal. % 10.25/10.49 (* end of lemma zenon_L628_ *) % 10.25/10.49 assert (zenon_L629_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H15e zenon_Hfa zenon_H104 zenon_Hf6 zenon_He9 zenon_H42 zenon_He5 zenon_Hfd. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.49 apply (zenon_L383_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.49 apply (zenon_L99_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.49 apply (zenon_L616_); trivial. % 10.25/10.49 apply (zenon_L103_); trivial. % 10.25/10.49 (* end of lemma zenon_L629_ *) % 10.25/10.49 assert (zenon_L630_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H191 zenon_H2f zenon_H177 zenon_Hfd zenon_H42 zenon_He9 zenon_Hf6 zenon_H104 zenon_H15e zenon_H281 zenon_H44 zenon_H1de zenon_H12a zenon_Hd3 zenon_H298 zenon_H1e5 zenon_H272 zenon_Hce zenon_Hbb zenon_He0 zenon_H2b9 zenon_H36 zenon_H2e4 zenon_H12d zenon_H284 zenon_Hdf zenon_Hda zenon_Hc6 zenon_H26e zenon_Hf4 zenon_H85 zenon_H1a3 zenon_H131 zenon_H99. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.25/10.49 exact (zenon_H2f zenon_H31). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.25/10.49 apply (zenon_L282_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.49 exact (zenon_H44 zenon_H46). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.49 apply (zenon_L89_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.49 exact (zenon_H44 zenon_H46). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.49 apply (zenon_L494_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.49 apply (zenon_L312_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.25/10.49 apply (zenon_L99_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.25/10.49 apply (zenon_L225_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.49 apply (zenon_L43_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.49 apply (zenon_L73_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.49 apply (zenon_L48_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.25/10.49 apply (zenon_L619_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.25/10.49 apply (zenon_L622_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.25/10.49 apply (zenon_L234_); trivial. % 10.25/10.49 apply (zenon_L522_); trivial. % 10.25/10.49 apply (zenon_L623_); trivial. % 10.25/10.49 apply (zenon_L220_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.49 apply (zenon_L99_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.49 apply (zenon_L91_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.49 apply (zenon_L494_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.49 apply (zenon_L312_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.49 apply (zenon_L627_); trivial. % 10.25/10.49 apply (zenon_L220_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.49 apply (zenon_L59_); trivial. % 10.25/10.49 apply (zenon_L628_); trivial. % 10.25/10.49 apply (zenon_L629_); trivial. % 10.25/10.49 apply (zenon_L110_); trivial. % 10.25/10.49 (* end of lemma zenon_L630_ *) % 10.25/10.49 assert (zenon_L631_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H15e zenon_Hba zenon_H14b zenon_H127 zenon_He9 zenon_H42 zenon_H198 zenon_H104. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.49 apply (zenon_L541_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.49 apply (zenon_L90_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.49 apply (zenon_L616_); trivial. % 10.25/10.49 apply (zenon_L135_); trivial. % 10.25/10.49 (* end of lemma zenon_L631_ *) % 10.25/10.49 assert (zenon_L632_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H12d zenon_H99 zenon_Hfd zenon_H85 zenon_Hf4 zenon_H36 zenon_Hf6 zenon_H2b9 zenon_He9 zenon_H127. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.49 apply (zenon_L58_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.49 apply (zenon_L312_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.49 apply (zenon_L623_); trivial. % 10.25/10.49 apply (zenon_L77_); trivial. % 10.25/10.49 (* end of lemma zenon_L632_ *) % 10.25/10.49 assert (zenon_L633_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H124 zenon_Hb9 zenon_Hf4 zenon_H36 zenon_H171 zenon_H163 zenon_H157 zenon_H198. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.49 apply (zenon_L59_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.49 apply (zenon_L107_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.49 exact (zenon_H163 zenon_H103). % 10.25/10.49 apply (zenon_L210_); trivial. % 10.25/10.49 (* end of lemma zenon_L633_ *) % 10.25/10.49 assert (zenon_L634_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H1a2 zenon_H2f zenon_H127 zenon_He9 zenon_H2b9 zenon_H85 zenon_Hfd zenon_H12d zenon_H99 zenon_H42 zenon_H124 zenon_Hb9 zenon_Hf4 zenon_H36 zenon_H171 zenon_H163 zenon_H157. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.25/10.49 exact (zenon_H2f zenon_H31). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.25/10.49 apply (zenon_L632_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.25/10.49 apply (zenon_L421_); trivial. % 10.25/10.49 apply (zenon_L633_); trivial. % 10.25/10.49 (* end of lemma zenon_L634_ *) % 10.25/10.49 assert (zenon_L635_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H281 zenon_H44 zenon_H104 zenon_H198 zenon_H42 zenon_He9 zenon_H127 zenon_H14b zenon_H15e zenon_Hfa zenon_Hf4 zenon_H131 zenon_H85. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.49 exact (zenon_H44 zenon_H46). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.49 apply (zenon_L631_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.49 apply (zenon_L59_); trivial. % 10.25/10.49 apply (zenon_L628_); trivial. % 10.25/10.49 (* end of lemma zenon_L635_ *) % 10.25/10.49 assert (zenon_L636_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H1b2 zenon_Hfa zenon_H101. % 10.25/10.49 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_H1b2. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_Hfa. % 10.25/10.49 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 10.25/10.49 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 10.25/10.49 congruence. % 10.25/10.49 apply zenon_Hbd. apply refl_equal. % 10.25/10.49 apply zenon_H102. apply sym_equal. exact zenon_H101. % 10.25/10.49 (* end of lemma zenon_L636_ *) % 10.25/10.49 assert (zenon_L637_ : (((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) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H28c zenon_Hc4 zenon_H101 zenon_H1b2 zenon_H136 zenon_H135 zenon_Hc0 zenon_H5a. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H28d ]. % 10.25/10.49 apply (zenon_L259_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_Hfa | zenon_intro zenon_H28e ]. % 10.25/10.49 apply (zenon_L636_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H152 ]. % 10.25/10.49 apply (zenon_L83_); trivial. % 10.25/10.49 apply (zenon_L384_); trivial. % 10.25/10.49 (* end of lemma zenon_L637_ *) % 10.25/10.49 assert (zenon_L638_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H12d zenon_Ha4 zenon_H99 zenon_H36 zenon_H198 zenon_H157 zenon_H163 zenon_H28c zenon_H1b2 zenon_H136 zenon_H135 zenon_Hc0 zenon_H5a zenon_H245 zenon_Hf4 zenon_H15e zenon_H14b zenon_H104 zenon_H44 zenon_H281 zenon_H42 zenon_H27c zenon_Hd3 zenon_H85 zenon_H124 zenon_He9 zenon_H127. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.49 apply (zenon_L486_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.49 apply (zenon_L312_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.49 apply (zenon_L635_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.49 apply (zenon_L77_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.49 apply (zenon_L322_); trivial. % 10.25/10.49 apply (zenon_L624_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.49 apply (zenon_L637_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.49 exact (zenon_H163 zenon_H103). % 10.25/10.49 apply (zenon_L210_); trivial. % 10.25/10.49 apply (zenon_L77_); trivial. % 10.25/10.49 (* end of lemma zenon_L638_ *) % 10.25/10.49 assert (zenon_L639_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H171 zenon_Hfd zenon_H2b9 zenon_H2f zenon_H1a2 zenon_H124 zenon_H85 zenon_Hd3 zenon_H27c zenon_H281 zenon_H44 zenon_H15e zenon_Hf4 zenon_H245 zenon_Hc0 zenon_H135 zenon_H1b2 zenon_H28c zenon_H163 zenon_H157 zenon_H36 zenon_H99 zenon_Ha4 zenon_H12d zenon_H14b zenon_H127 zenon_He9 zenon_H42 zenon_H198 zenon_H104. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.49 exact (zenon_H44 zenon_H46). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.49 apply (zenon_L631_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.49 apply (zenon_L634_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.49 apply (zenon_L638_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.49 apply (zenon_L90_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.49 apply (zenon_L616_); trivial. % 10.25/10.49 apply (zenon_L135_); trivial. % 10.25/10.49 (* end of lemma zenon_L639_ *) % 10.25/10.49 assert (zenon_L640_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H244 zenon_H13d zenon_H13c zenon_H104 zenon_H198 zenon_H42 zenon_He9 zenon_H14b zenon_H12d zenon_Ha4 zenon_H99 zenon_H36 zenon_H157 zenon_H163 zenon_H28c zenon_H1b2 zenon_H135 zenon_Hc0 zenon_H245 zenon_Hf4 zenon_H15e zenon_H44 zenon_H281 zenon_H27c zenon_H85 zenon_H124 zenon_H1a2 zenon_H2f zenon_H2b9 zenon_H171 zenon_H1f9 zenon_Hfd zenon_Hd3. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.25/10.49 apply (zenon_L85_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.25/10.49 apply (zenon_L639_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.25/10.49 exact (zenon_H1f9 zenon_H1ed). % 10.25/10.49 apply (zenon_L353_); trivial. % 10.25/10.49 (* end of lemma zenon_L640_ *) % 10.25/10.49 assert (zenon_L641_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H15e zenon_Hba zenon_H14b zenon_H127 zenon_Hfd zenon_Hcd zenon_H198 zenon_H104. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.49 apply (zenon_L541_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.49 apply (zenon_L90_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.49 apply (zenon_L91_); trivial. % 10.25/10.49 apply (zenon_L135_); trivial. % 10.25/10.49 (* end of lemma zenon_L641_ *) % 10.25/10.49 assert (zenon_L642_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H244 zenon_H130 zenon_H44 zenon_H2f zenon_H42 zenon_H47 zenon_H303 zenon_H104 zenon_H198 zenon_Hcd zenon_H14b zenon_Hba zenon_H15e zenon_H1f9 zenon_Hfd zenon_Hd3. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.25/10.49 apply (zenon_L609_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.25/10.49 apply (zenon_L641_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.25/10.49 exact (zenon_H1f9 zenon_H1ed). % 10.25/10.49 apply (zenon_L353_); trivial. % 10.25/10.49 (* end of lemma zenon_L642_ *) % 10.25/10.49 assert (zenon_L643_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H1a3 zenon_Hfa zenon_H135 zenon_H13d zenon_H12d zenon_H99 zenon_H28c zenon_H1b2 zenon_Hc0 zenon_H245 zenon_H27c zenon_H1a2 zenon_H2b9 zenon_H289 zenon_He9 zenon_H85 zenon_H131 zenon_H124 zenon_H36 zenon_H171 zenon_H163 zenon_H157 zenon_H244 zenon_H130 zenon_H44 zenon_H2f zenon_H42 zenon_H47 zenon_H303 zenon_H104 zenon_H14b zenon_H15e zenon_H1f9 zenon_Hfd zenon_Hd3 zenon_H281 zenon_H198 zenon_Hf4. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.49 exact (zenon_H44 zenon_H46). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.49 exact (zenon_H44 zenon_H46). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.49 apply (zenon_L541_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.25/10.49 apply (zenon_L541_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.25/10.49 apply (zenon_L640_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.25/10.49 apply (zenon_L354_); trivial. % 10.25/10.49 apply (zenon_L575_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.49 apply (zenon_L616_); trivial. % 10.25/10.49 apply (zenon_L135_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.49 apply (zenon_L59_); trivial. % 10.25/10.49 apply (zenon_L628_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.49 exact (zenon_H44 zenon_H46). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.49 apply (zenon_L642_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.49 apply (zenon_L633_); trivial. % 10.25/10.49 apply (zenon_L628_); trivial. % 10.25/10.49 apply (zenon_L143_); trivial. % 10.25/10.49 (* end of lemma zenon_L643_ *) % 10.25/10.49 assert (zenon_L644_ : (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H26e zenon_Hc6 zenon_Hda zenon_Hdf zenon_H284 zenon_H2e4 zenon_He0 zenon_Hbb zenon_Hce zenon_H272 zenon_H1e5 zenon_H298 zenon_H12a zenon_H1de zenon_H191 zenon_H177 zenon_Hf4 zenon_H281 zenon_Hd3 zenon_Hfd zenon_H1f9 zenon_H15e zenon_H14b zenon_H104 zenon_H303 zenon_H47 zenon_H42 zenon_H2f zenon_H44 zenon_H130 zenon_H244 zenon_H157 zenon_H163 zenon_H171 zenon_H36 zenon_H124 zenon_H85 zenon_He9 zenon_H289 zenon_H2b9 zenon_H1a2 zenon_H27c zenon_H245 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_H12d zenon_H13d zenon_H135 zenon_H1a3 zenon_H131 zenon_H99. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.25/10.49 exact (zenon_H2f zenon_H31). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.25/10.49 apply (zenon_L630_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.25/10.49 apply (zenon_L421_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.25/10.49 exact (zenon_H2f zenon_H31). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.25/10.49 apply (zenon_L282_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.25/10.49 apply (zenon_L643_); trivial. % 10.25/10.49 apply (zenon_L110_); trivial. % 10.25/10.49 (* end of lemma zenon_L644_ *) % 10.25/10.49 assert (zenon_L645_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H244 zenon_H130 zenon_H44 zenon_H2f zenon_H42 zenon_H47 zenon_H303 zenon_H128 zenon_He9 zenon_H1f9 zenon_H17c zenon_H29d. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.25/10.49 apply (zenon_L609_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.25/10.49 apply (zenon_L77_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.25/10.49 exact (zenon_H1f9 zenon_H1ed). % 10.25/10.49 apply (zenon_L395_); trivial. % 10.25/10.49 (* end of lemma zenon_L645_ *) % 10.25/10.49 assert (zenon_L646_ : (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((e1) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H99 zenon_H1a3 zenon_H135 zenon_H13d zenon_H12d zenon_H28c zenon_H1b2 zenon_Hc0 zenon_H245 zenon_H1a2 zenon_H2b9 zenon_H289 zenon_H124 zenon_H36 zenon_H171 zenon_H163 zenon_H157 zenon_H104 zenon_H14b zenon_H15e zenon_Hfd zenon_H281 zenon_Hf4 zenon_H177 zenon_H191 zenon_H1de zenon_H12a zenon_H298 zenon_H1e5 zenon_H272 zenon_Hce zenon_Hbb zenon_He0 zenon_H2e4 zenon_H284 zenon_Hdf zenon_Hda zenon_Hc6 zenon_H26e zenon_H29d zenon_H17c zenon_H1f9 zenon_He9 zenon_H303 zenon_H47 zenon_H2f zenon_H44 zenon_H130 zenon_H244 zenon_H42 zenon_H27c zenon_Hd3 zenon_H85. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.49 apply (zenon_L644_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.49 apply (zenon_L645_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.49 apply (zenon_L322_); trivial. % 10.25/10.49 apply (zenon_L624_); trivial. % 10.25/10.49 (* end of lemma zenon_L646_ *) % 10.25/10.49 assert (zenon_L647_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e2))) -> ((op (e3) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H12d zenon_H2b9 zenon_H12a zenon_Hf6 zenon_H36 zenon_H85 zenon_Hd3 zenon_H298 zenon_H104 zenon_H158 zenon_H99 zenon_Hf4 zenon_H1e5 zenon_He9 zenon_H272 zenon_Hcd zenon_Hce zenon_Hba zenon_Hbb zenon_He0 zenon_Hfd. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.49 apply (zenon_L58_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.49 apply (zenon_L312_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.49 apply (zenon_L627_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.25/10.49 apply (zenon_L89_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.25/10.49 apply (zenon_L310_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.25/10.49 apply (zenon_L279_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.25/10.49 apply (zenon_L99_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.25/10.49 apply (zenon_L225_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.25/10.49 apply (zenon_L626_); trivial. % 10.25/10.49 apply (zenon_L199_); trivial. % 10.25/10.49 (* end of lemma zenon_L647_ *) % 10.25/10.49 assert (zenon_L648_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_He0 zenon_H135 zenon_Hd3 zenon_H1f9 zenon_H136 zenon_H2e4 zenon_H12d zenon_Hce zenon_H272 zenon_H284 zenon_H42 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_Hdf zenon_H36 zenon_Hcd zenon_Hda zenon_Hc6 zenon_H298 zenon_H85 zenon_H244 zenon_H130 zenon_H5a zenon_H252 zenon_Hfd zenon_H186 zenon_H17a zenon_He9. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.49 apply (zenon_L83_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.49 apply (zenon_L611_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.49 apply (zenon_L48_); trivial. % 10.25/10.49 apply (zenon_L620_); trivial. % 10.25/10.49 (* end of lemma zenon_L648_ *) % 10.25/10.49 assert (zenon_L649_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H245 zenon_H136 zenon_H29d zenon_H17c zenon_H1f9 zenon_He9 zenon_H303 zenon_H47 zenon_H2f zenon_H44 zenon_H130 zenon_H244 zenon_H42 zenon_H27c zenon_Hd3 zenon_H85. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.49 apply (zenon_L628_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.49 apply (zenon_L645_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.49 apply (zenon_L322_); trivial. % 10.25/10.49 apply (zenon_L624_); trivial. % 10.25/10.49 (* end of lemma zenon_L649_ *) % 10.25/10.49 assert (zenon_L650_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_He0 zenon_H135 zenon_Hfd zenon_H1f9 zenon_H136 zenon_H244 zenon_H36 zenon_H42 zenon_H2e4 zenon_H12d zenon_Hce zenon_Hcd zenon_H272 zenon_He9 zenon_H1e5 zenon_Hf4 zenon_H99 zenon_H158 zenon_H104 zenon_H298 zenon_Hd3 zenon_H85. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.49 apply (zenon_L83_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.49 apply (zenon_L611_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.49 apply (zenon_L48_); trivial. % 10.25/10.49 apply (zenon_L625_); trivial. % 10.25/10.49 (* end of lemma zenon_L650_ *) % 10.25/10.49 assert (zenon_L651_ : (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (((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) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_Hf4 zenon_H198 zenon_H281 zenon_H15e zenon_H14b zenon_H104 zenon_H303 zenon_H47 zenon_H2f zenon_H44 zenon_H130 zenon_H157 zenon_H163 zenon_H171 zenon_H36 zenon_H124 zenon_H289 zenon_H2b9 zenon_H1a2 zenon_H245 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_H99 zenon_H12d zenon_H13d zenon_H135 zenon_Hfa zenon_H1a3 zenon_Hfd zenon_H1f9 zenon_He9 zenon_H136 zenon_H244 zenon_H42 zenon_H27c zenon_Hd3 zenon_H85. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.25/10.49 apply (zenon_L643_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.25/10.49 apply (zenon_L610_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.25/10.49 apply (zenon_L322_); trivial. % 10.25/10.49 apply (zenon_L624_); trivial. % 10.25/10.49 (* end of lemma zenon_L651_ *) % 10.25/10.49 assert (zenon_L652_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.25/10.49 do 0 intro. intros zenon_He0 zenon_Hd3 zenon_Hfd zenon_H1f9 zenon_He9 zenon_H244 zenon_H85 zenon_H36 zenon_H99 zenon_H42 zenon_H2e4 zenon_H12d zenon_Hf4 zenon_Hfa zenon_H15e zenon_H130 zenon_H44 zenon_H2f zenon_H47 zenon_H303 zenon_H135 zenon_H14b zenon_H13d zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H171 zenon_H2f5 zenon_H52 zenon_H289 zenon_H198 zenon_H104 zenon_H281 zenon_Hce zenon_Hcd zenon_Hdd zenon_Hc6. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.49 apply (zenon_L59_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.49 apply (zenon_L612_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.49 apply (zenon_L48_); trivial. % 10.25/10.49 apply (zenon_L238_); trivial. % 10.25/10.49 (* end of lemma zenon_L652_ *) % 10.25/10.49 assert (zenon_L653_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 10.25/10.49 do 0 intro. intros zenon_Hdf zenon_Hda zenon_H124 zenon_Hc6 zenon_Hcd zenon_Hce zenon_H281 zenon_H104 zenon_H289 zenon_H52 zenon_H2f5 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H1de zenon_H12a zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_H13d zenon_H14b zenon_H135 zenon_H303 zenon_H47 zenon_H2f zenon_H44 zenon_H130 zenon_H15e zenon_Hf4 zenon_H12d zenon_H2e4 zenon_H42 zenon_H99 zenon_H85 zenon_H244 zenon_He9 zenon_H1f9 zenon_Hfd zenon_Hd3 zenon_He0 zenon_H36 zenon_H171 zenon_H163 zenon_H157 zenon_H198. % 10.25/10.49 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.49 apply (zenon_L642_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.49 apply (zenon_L310_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.49 apply (zenon_L50_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.49 apply (zenon_L652_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.49 apply (zenon_L107_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.49 exact (zenon_H163 zenon_H103). % 10.25/10.49 apply (zenon_L210_); trivial. % 10.25/10.49 (* end of lemma zenon_L653_ *) % 10.25/10.49 assert (zenon_L654_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H244 zenon_H136 zenon_Hfd zenon_H14b zenon_H119 zenon_H1f9 zenon_H159 zenon_Hd5. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.25/10.49 apply (zenon_L255_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.25/10.49 apply (zenon_L90_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.25/10.49 exact (zenon_H1f9 zenon_H1ed). % 10.25/10.49 apply (zenon_L397_); trivial. % 10.25/10.49 (* end of lemma zenon_L654_ *) % 10.25/10.49 assert (zenon_L655_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e3) (e2)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H15b zenon_Hd3 zenon_H135 zenon_H100 zenon_H51 zenon_H244 zenon_H136 zenon_Hfd zenon_H14b zenon_H119 zenon_H1f9 zenon_Hd5. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.25/10.49 apply (zenon_L354_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.25/10.49 apply (zenon_L212_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.25/10.49 apply (zenon_L60_); trivial. % 10.25/10.49 apply (zenon_L654_); trivial. % 10.25/10.49 (* end of lemma zenon_L655_ *) % 10.25/10.49 assert (zenon_L656_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e2)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H12d zenon_H2e4 zenon_H42 zenon_H99 zenon_H36 zenon_Hc1 zenon_H1b2 zenon_H244 zenon_H136 zenon_He9 zenon_H1f9 zenon_Hfd zenon_Hd3. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.49 apply (zenon_L494_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.49 apply (zenon_L312_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.49 apply (zenon_L259_); trivial. % 10.25/10.49 apply (zenon_L610_); trivial. % 10.25/10.49 (* end of lemma zenon_L656_ *) % 10.25/10.49 assert (zenon_L657_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (~((e2) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H12d zenon_H2e4 zenon_H42 zenon_H99 zenon_H36 zenon_Hc1 zenon_H1b2 zenon_H244 zenon_H133 zenon_H104 zenon_He9 zenon_H1f9 zenon_H52 zenon_Hfd. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.49 apply (zenon_L494_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.49 apply (zenon_L312_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.49 apply (zenon_L259_); trivial. % 10.25/10.49 apply (zenon_L614_); trivial. % 10.25/10.49 (* end of lemma zenon_L657_ *) % 10.25/10.49 assert (zenon_L658_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_Hc1 zenon_H152 zenon_He9. % 10.25/10.49 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.25/10.49 cut (((e3) = (e3)) = ((e0) = (e3))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_He9. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_Hea. % 10.25/10.49 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.25/10.49 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 10.25/10.49 congruence. % 10.25/10.49 cut (((op (e2) (e0)) = (e0)) = ((e3) = (e0))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_Hec. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_Hc1. % 10.25/10.49 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.49 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 10.25/10.49 congruence. % 10.25/10.49 exact (zenon_H153 zenon_H152). % 10.25/10.49 apply zenon_H84. apply refl_equal. % 10.25/10.49 apply zenon_Heb. apply refl_equal. % 10.25/10.49 apply zenon_Heb. apply refl_equal. % 10.25/10.49 (* end of lemma zenon_L658_ *) % 10.25/10.49 assert (zenon_L659_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H303 zenon_Hc1 zenon_Hc0 zenon_H2f zenon_H44 zenon_H13b zenon_H130. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H1f | zenon_intro zenon_H304 ]. % 10.25/10.49 apply (zenon_L44_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H31 | zenon_intro zenon_H305 ]. % 10.25/10.49 exact (zenon_H2f zenon_H31). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H46 | zenon_intro zenon_H5a ]. % 10.25/10.49 exact (zenon_H44 zenon_H46). % 10.25/10.49 apply (zenon_L133_); trivial. % 10.25/10.49 (* end of lemma zenon_L659_ *) % 10.25/10.49 assert (zenon_L660_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H5f zenon_H36 zenon_H104. % 10.25/10.49 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H56. zenon_intro zenon_H60. % 10.25/10.49 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H58. zenon_intro zenon_Hf2. % 10.25/10.49 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.25/10.49 apply (zenon_L225_); trivial. % 10.25/10.49 (* end of lemma zenon_L660_ *) % 10.25/10.49 assert (zenon_L661_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e3)) = (e2))) -> ((op (e2) (e2)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H12a zenon_Hf6 zenon_H104 zenon_H36 zenon_H122 zenon_Hfc zenon_Hf4 zenon_Hfa zenon_He0 zenon_Hfd zenon_H252. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.25/10.49 apply (zenon_L99_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.25/10.49 apply (zenon_L225_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.25/10.49 apply (zenon_L74_); trivial. % 10.25/10.49 apply (zenon_L199_); trivial. % 10.25/10.49 (* end of lemma zenon_L661_ *) % 10.25/10.49 assert (zenon_L662_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H15e zenon_H58 zenon_H104 zenon_Hf6 zenon_Hfd zenon_Hcd zenon_H56 zenon_He9. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.49 exact (zenon_H58 zenon_H5a). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.49 apply (zenon_L99_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.49 apply (zenon_L91_); trivial. % 10.25/10.49 apply (zenon_L324_); trivial. % 10.25/10.49 (* end of lemma zenon_L662_ *) % 10.25/10.49 assert (zenon_L663_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H56 zenon_He5 zenon_H85. % 10.25/10.49 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H86 | zenon_intro zenon_H87 ]. % 10.25/10.49 cut (((e2) = (e2)) = ((e0) = (e2))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_H85. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_H86. % 10.25/10.49 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.25/10.49 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 10.25/10.49 congruence. % 10.25/10.49 cut (((op (e0) (e3)) = (e0)) = ((e2) = (e0))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_H88. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_H56. % 10.25/10.49 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.49 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 10.25/10.49 congruence. % 10.25/10.49 exact (zenon_H1a1 zenon_He5). % 10.25/10.49 apply zenon_H84. apply refl_equal. % 10.25/10.49 apply zenon_H87. apply refl_equal. % 10.25/10.49 apply zenon_H87. apply refl_equal. % 10.25/10.49 (* end of lemma zenon_L663_ *) % 10.25/10.49 assert (zenon_L664_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H1a3 zenon_H133 zenon_Hf4 zenon_He9 zenon_Hfd zenon_Hf6 zenon_H104 zenon_H58 zenon_H15e zenon_H56 zenon_H85. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.49 exact (zenon_H58 zenon_H5a). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.49 apply (zenon_L99_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.49 apply (zenon_L565_); trivial. % 10.25/10.49 apply (zenon_L324_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.49 apply (zenon_L89_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.49 apply (zenon_L662_); trivial. % 10.25/10.49 apply (zenon_L663_); trivial. % 10.25/10.49 (* end of lemma zenon_L664_ *) % 10.25/10.49 assert (zenon_L665_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H303 zenon_H5b zenon_H56 zenon_H2f zenon_H16e zenon_H13c zenon_H58. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H1f | zenon_intro zenon_H304 ]. % 10.25/10.49 apply (zenon_L16_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H31 | zenon_intro zenon_H305 ]. % 10.25/10.49 exact (zenon_H2f zenon_H31). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H46 | zenon_intro zenon_H5a ]. % 10.25/10.49 apply (zenon_L556_); trivial. % 10.25/10.49 exact (zenon_H58 zenon_H5a). % 10.25/10.49 (* end of lemma zenon_L665_ *) % 10.25/10.49 assert (zenon_L666_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H61 zenon_H51 zenon_Hfd. % 10.25/10.49 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H56. zenon_intro zenon_H62. % 10.25/10.49 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H58. zenon_intro zenon_H1d3. % 10.25/10.49 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.25/10.49 apply (zenon_L60_); trivial. % 10.25/10.49 (* end of lemma zenon_L666_ *) % 10.25/10.49 assert (zenon_L667_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> (~((op (e2) (e3)) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_He0 zenon_H152 zenon_Hc4 zenon_H85 zenon_Hfd zenon_H61 zenon_H122. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.25/10.49 apply (zenon_L92_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.25/10.49 apply (zenon_L45_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.25/10.49 apply (zenon_L666_); trivial. % 10.25/10.49 exact (zenon_H122 zenon_Hd4). % 10.25/10.49 (* end of lemma zenon_L667_ *) % 10.25/10.49 assert (zenon_L668_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (e2))) -> (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.25/10.49 do 0 intro. intros zenon_Hca zenon_H122 zenon_H61 zenon_Hfd zenon_H85 zenon_H152 zenon_He0 zenon_He9 zenon_Hfc zenon_H157 zenon_H56. % 10.25/10.49 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.25/10.49 apply (zenon_L658_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.25/10.49 apply (zenon_L667_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.25/10.49 apply (zenon_L319_); trivial. % 10.25/10.49 apply (zenon_L209_); trivial. % 10.25/10.49 (* end of lemma zenon_L668_ *) % 10.25/10.49 assert (zenon_L669_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H18a zenon_H13b zenon_H104 zenon_H36 zenon_H262 zenon_H16e zenon_H27c zenon_H1e5. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.25/10.49 apply (zenon_L123_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.25/10.49 apply (zenon_L208_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.25/10.49 apply (zenon_L320_); trivial. % 10.25/10.49 exact (zenon_H1e5 zenon_H189). % 10.25/10.49 (* end of lemma zenon_L669_ *) % 10.25/10.49 assert (zenon_L670_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H56 zenon_H198 zenon_H99. % 10.25/10.49 elim (classic ((e1) = (e1))); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H98 ]. % 10.25/10.49 cut (((e1) = (e1)) = ((e0) = (e1))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_H99. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_Hf7. % 10.25/10.49 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.25/10.49 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 10.25/10.49 congruence. % 10.25/10.49 cut (((op (e0) (e3)) = (e0)) = ((e1) = (e0))). % 10.25/10.49 intro zenon_D_pnotp. % 10.25/10.49 apply zenon_Hf8. % 10.25/10.49 rewrite <- zenon_D_pnotp. % 10.25/10.49 exact zenon_H56. % 10.25/10.49 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.25/10.49 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H307]. % 10.25/10.49 congruence. % 10.25/10.49 exact (zenon_H307 zenon_H198). % 10.25/10.49 apply zenon_H84. apply refl_equal. % 10.25/10.49 apply zenon_H98. apply refl_equal. % 10.25/10.49 apply zenon_H98. apply refl_equal. % 10.25/10.49 (* end of lemma zenon_L670_ *) % 10.25/10.49 assert (zenon_L671_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H1ac zenon_H36 zenon_H99. % 10.25/10.49 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_Hb9. zenon_intro zenon_H1ad. % 10.25/10.49 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H71. zenon_intro zenon_H24. % 10.25/10.49 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.25/10.49 apply (zenon_L312_); trivial. % 10.25/10.49 (* end of lemma zenon_L671_ *) % 10.25/10.49 assert (zenon_L672_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 10.25/10.49 do 0 intro. intros zenon_H1b0 zenon_H287 zenon_H51. % 10.25/10.49 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb9. zenon_intro zenon_H1b1. % 10.25/10.49 apply (zenon_L299_); trivial. % 10.25/10.49 (* end of lemma zenon_L672_ *) % 10.25/10.49 assert (zenon_L673_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e2)) = (e3))) -> ((op (e3) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H1a3 zenon_H27c zenon_H1a2 zenon_H104 zenon_Hfd zenon_H127 zenon_H14b zenon_H157 zenon_H163 zenon_H28c zenon_H1b2 zenon_H135 zenon_Hc0 zenon_He0 zenon_H85 zenon_H36 zenon_H99 zenon_H42 zenon_H2e4 zenon_H12d zenon_H15e zenon_H130 zenon_H44 zenon_H2f zenon_H47 zenon_H303 zenon_H13d zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H1de zenon_H2ea zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H171 zenon_H2f5 zenon_H52 zenon_H289 zenon_H281 zenon_Hce zenon_Hc6 zenon_H124 zenon_Hda zenon_Hdf zenon_H244 zenon_He9 zenon_H1f9 zenon_Hd3 zenon_Hf4. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.25/10.49 exact (zenon_H2f zenon_H31). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.25/10.49 apply (zenon_L632_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.25/10.49 apply (zenon_L421_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.25/10.49 exact (zenon_H44 zenon_H46). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.25/10.49 apply (zenon_L639_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.25/10.49 exact (zenon_H44 zenon_H46). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.25/10.49 apply (zenon_L631_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.25/10.49 apply (zenon_L633_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.25/10.49 apply (zenon_L494_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.25/10.49 apply (zenon_L312_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.25/10.49 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.25/10.49 apply (zenon_L541_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.25/10.49 apply (zenon_L310_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.25/10.49 apply (zenon_L50_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.25/10.49 apply (zenon_L652_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.25/10.49 apply (zenon_L637_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.25/10.49 exact (zenon_H163 zenon_H103). % 10.25/10.49 apply (zenon_L210_); trivial. % 10.25/10.49 apply (zenon_L610_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.25/10.49 apply (zenon_L90_); trivial. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.25/10.49 apply (zenon_L91_); trivial. % 10.25/10.49 apply (zenon_L135_); trivial. % 10.25/10.49 apply (zenon_L143_); trivial. % 10.25/10.49 (* end of lemma zenon_L673_ *) % 10.25/10.49 assert (zenon_L674_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.25/10.49 do 0 intro. intros zenon_H15e zenon_H58 zenon_H14b zenon_H127 zenon_H104 zenon_H16e zenon_H56 zenon_He9. % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.25/10.49 exact (zenon_H58 zenon_H5a). % 10.25/10.49 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.50 apply (zenon_L90_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.50 apply (zenon_L105_); trivial. % 10.36/10.50 apply (zenon_L324_); trivial. % 10.36/10.50 (* end of lemma zenon_L674_ *) % 10.36/10.50 assert (zenon_L675_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((op (e0) (e0)) = (e1))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H1b7 zenon_H2f. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H163. zenon_intro zenon_H2e. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.36/10.50 exact (zenon_H2f zenon_H31). % 10.36/10.50 (* end of lemma zenon_L675_ *) % 10.36/10.50 assert (zenon_L676_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H290 zenon_H241 zenon_H278 zenon_H163 zenon_Hd4 zenon_H28f zenon_Hff. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H74 | zenon_intro zenon_H291 ]. % 10.36/10.50 apply (zenon_L298_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H103 | zenon_intro zenon_H292 ]. % 10.36/10.50 exact (zenon_H163 zenon_H103). % 10.36/10.50 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfc ]. % 10.36/10.50 apply (zenon_L264_); trivial. % 10.36/10.50 exact (zenon_Hff zenon_Hfc). % 10.36/10.50 (* end of lemma zenon_L676_ *) % 10.36/10.50 assert (zenon_L677_ : ((op (e2) (e2)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H74 zenon_H42 zenon_Hce. % 10.36/10.50 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hd0 ]. % 10.36/10.50 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 10.36/10.50 intro zenon_D_pnotp. % 10.36/10.50 apply zenon_Hce. % 10.36/10.50 rewrite <- zenon_D_pnotp. % 10.36/10.50 exact zenon_Hcf. % 10.36/10.50 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.36/10.50 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 10.36/10.50 congruence. % 10.36/10.50 cut (((op (e2) (e2)) = (e0)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 10.36/10.50 intro zenon_D_pnotp. % 10.36/10.50 apply zenon_Hd1. % 10.36/10.50 rewrite <- zenon_D_pnotp. % 10.36/10.50 exact zenon_H74. % 10.36/10.50 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H306]. % 10.36/10.50 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.36/10.50 congruence. % 10.36/10.50 apply zenon_Hd0. apply refl_equal. % 10.36/10.50 apply zenon_H306. apply sym_equal. exact zenon_H42. % 10.36/10.50 apply zenon_Hd0. apply refl_equal. % 10.36/10.50 apply zenon_Hd0. apply refl_equal. % 10.36/10.50 (* end of lemma zenon_L677_ *) % 10.36/10.50 assert (zenon_L678_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e3)) -> False). % 10.36/10.50 do 0 intro. intros zenon_H2bc zenon_Hce zenon_H74 zenon_H284 zenon_H198 zenon_Hdb zenon_Hda zenon_H17a. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H42 | zenon_intro zenon_H2bd ]. % 10.36/10.50 apply (zenon_L677_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H16e | zenon_intro zenon_H2be ]. % 10.36/10.50 apply (zenon_L258_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_Hcd | zenon_intro zenon_H150 ]. % 10.36/10.50 apply (zenon_L50_); trivial. % 10.36/10.50 apply (zenon_L308_); trivial. % 10.36/10.50 (* end of lemma zenon_L678_ *) % 10.36/10.50 assert (zenon_L679_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> False). % 10.36/10.50 do 0 intro. intros zenon_H1c9 zenon_H28f zenon_H51. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_Hd4. zenon_intro zenon_H1ca. % 10.36/10.50 apply (zenon_L264_); trivial. % 10.36/10.50 (* end of lemma zenon_L679_ *) % 10.36/10.50 assert (zenon_L680_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (e3))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H290 zenon_H17a zenon_Hda zenon_Hdb zenon_H198 zenon_H284 zenon_Hce zenon_H2bc zenon_H163 zenon_H28f zenon_H1c9 zenon_Hff. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H74 | zenon_intro zenon_H291 ]. % 10.36/10.50 apply (zenon_L678_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H103 | zenon_intro zenon_H292 ]. % 10.36/10.50 exact (zenon_H163 zenon_H103). % 10.36/10.50 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfc ]. % 10.36/10.50 apply (zenon_L679_); trivial. % 10.36/10.50 exact (zenon_Hff zenon_Hfc). % 10.36/10.50 (* end of lemma zenon_L680_ *) % 10.36/10.50 assert (zenon_L681_ : (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e1)) -> False). % 10.36/10.50 do 0 intro. intros zenon_H2a8 zenon_H5a zenon_H47 zenon_H1c9 zenon_H28f zenon_H163 zenon_H2bc zenon_Hce zenon_H284 zenon_H198 zenon_Hdb zenon_Hda zenon_H290 zenon_Hff zenon_H104 zenon_H187. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.36/10.50 apply (zenon_L355_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.36/10.50 apply (zenon_L680_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.36/10.50 exact (zenon_Hff zenon_Hfc). % 10.36/10.50 apply (zenon_L219_); trivial. % 10.36/10.50 (* end of lemma zenon_L681_ *) % 10.36/10.50 assert (zenon_L682_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.50 do 0 intro. intros zenon_Hdf zenon_H46 zenon_H94 zenon_Hf4 zenon_H104 zenon_Hff zenon_H290 zenon_Hda zenon_H198 zenon_H284 zenon_Hce zenon_H2bc zenon_H163 zenon_H28f zenon_H1c9 zenon_H47 zenon_H5a zenon_H2a8 zenon_H36 zenon_H9c zenon_H293 zenon_Hd4 zenon_Hc6. % 10.36/10.50 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.50 apply (zenon_L511_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.50 apply (zenon_L310_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.36/10.50 apply (zenon_L258_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.36/10.50 apply (zenon_L36_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.36/10.50 exact (zenon_H163 zenon_H103). % 10.36/10.50 apply (zenon_L681_); trivial. % 10.36/10.50 apply (zenon_L238_); trivial. % 10.36/10.50 (* end of lemma zenon_L682_ *) % 10.36/10.50 assert (zenon_L683_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.50 do 0 intro. intros zenon_Hdf zenon_Hf4 zenon_H163 zenon_H28c zenon_Hc4 zenon_H1b2 zenon_H136 zenon_H135 zenon_Hc0 zenon_H5a zenon_H2a8 zenon_H47 zenon_H1c9 zenon_H28f zenon_H2bc zenon_Hce zenon_Hda zenon_H290 zenon_Hff zenon_H293 zenon_H284 zenon_H198 zenon_H9c zenon_H36 zenon_H287 zenon_H104 zenon_H124 zenon_Hd4 zenon_Hc6. % 10.36/10.50 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.50 apply (zenon_L541_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.50 apply (zenon_L310_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.36/10.50 apply (zenon_L355_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.36/10.50 apply (zenon_L680_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.36/10.50 exact (zenon_Hff zenon_Hfc). % 10.36/10.50 apply (zenon_L557_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.50 apply (zenon_L637_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.50 exact (zenon_H163 zenon_H103). % 10.36/10.50 apply (zenon_L269_); trivial. % 10.36/10.50 apply (zenon_L238_); trivial. % 10.36/10.50 (* end of lemma zenon_L683_ *) % 10.36/10.50 assert (zenon_L684_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.36/10.50 do 0 intro. intros zenon_H281 zenon_H94 zenon_H1cb zenon_H12d zenon_H85 zenon_Ha4 zenon_H99 zenon_Hc6 zenon_Hd4 zenon_H124 zenon_H104 zenon_H287 zenon_H36 zenon_H9c zenon_H198 zenon_H284 zenon_H293 zenon_Hff zenon_H290 zenon_Hda zenon_Hce zenon_H2bc zenon_H28f zenon_H1c9 zenon_H47 zenon_H2a8 zenon_H5a zenon_Hc0 zenon_H135 zenon_H1b2 zenon_H28c zenon_H163 zenon_Hf4 zenon_Hdf zenon_He9 zenon_H127. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.50 apply (zenon_L682_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.50 apply (zenon_L541_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.50 apply (zenon_L162_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.50 apply (zenon_L486_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.50 apply (zenon_L312_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.50 apply (zenon_L683_); trivial. % 10.36/10.50 apply (zenon_L77_); trivial. % 10.36/10.50 (* end of lemma zenon_L684_ *) % 10.36/10.50 assert (zenon_L685_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H298 zenon_H127 zenon_He9 zenon_Hdf zenon_H163 zenon_H28c zenon_H1b2 zenon_H135 zenon_Hc0 zenon_H5a zenon_H2a8 zenon_H47 zenon_H1c9 zenon_H28f zenon_H2bc zenon_Hce zenon_Hda zenon_H290 zenon_Hff zenon_H293 zenon_H284 zenon_H9c zenon_H287 zenon_H104 zenon_H124 zenon_Hc6 zenon_Ha4 zenon_H85 zenon_H12d zenon_H1cb zenon_H94 zenon_H281 zenon_H115 zenon_H36 zenon_Hd4 zenon_Hf4 zenon_H79 zenon_H99. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.36/10.50 apply (zenon_L684_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.36/10.50 apply (zenon_L65_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.36/10.50 apply (zenon_L269_); trivial. % 10.36/10.50 apply (zenon_L273_); trivial. % 10.36/10.50 (* end of lemma zenon_L685_ *) % 10.36/10.50 assert (zenon_L686_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H245 zenon_H1f zenon_H130 zenon_H278 zenon_H298 zenon_H127 zenon_He9 zenon_Hdf zenon_H163 zenon_H28c zenon_H1b2 zenon_H135 zenon_Hc0 zenon_H5a zenon_H2a8 zenon_H47 zenon_H1c9 zenon_H28f zenon_H2bc zenon_Hce zenon_Hda zenon_H290 zenon_Hff zenon_H293 zenon_H284 zenon_H9c zenon_H287 zenon_H104 zenon_H124 zenon_Hc6 zenon_Ha4 zenon_H85 zenon_H12d zenon_H1cb zenon_H94 zenon_H281 zenon_H115 zenon_H36 zenon_Hd4 zenon_Hf4 zenon_H99. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.50 apply (zenon_L81_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.50 apply (zenon_L77_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.50 apply (zenon_L676_); trivial. % 10.36/10.50 apply (zenon_L685_); trivial. % 10.36/10.50 (* end of lemma zenon_L686_ *) % 10.36/10.50 assert (zenon_L687_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.36/10.50 do 0 intro. intros zenon_H2b9 zenon_H99 zenon_Hd4 zenon_H115 zenon_H281 zenon_H94 zenon_H1cb zenon_H12d zenon_Hc6 zenon_H124 zenon_H104 zenon_H287 zenon_H9c zenon_H284 zenon_H293 zenon_Hff zenon_H290 zenon_Hda zenon_Hce zenon_H2bc zenon_H28f zenon_H1c9 zenon_H47 zenon_H2a8 zenon_H5a zenon_Hc0 zenon_H135 zenon_H1b2 zenon_H28c zenon_H163 zenon_Hdf zenon_He9 zenon_H298 zenon_H278 zenon_H130 zenon_H1f zenon_H245 zenon_H36 zenon_Hf4 zenon_Hc4 zenon_H85 zenon_Hfd zenon_H127. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.50 apply (zenon_L686_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.50 apply (zenon_L310_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.50 apply (zenon_L45_); trivial. % 10.36/10.50 apply (zenon_L199_); trivial. % 10.36/10.50 (* end of lemma zenon_L687_ *) % 10.36/10.50 assert (zenon_L688_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.50 do 0 intro. intros zenon_Hdf zenon_H5a zenon_Hf4 zenon_H104 zenon_Hff zenon_H290 zenon_Hda zenon_H198 zenon_H284 zenon_Hce zenon_H2bc zenon_H163 zenon_H28f zenon_H1c9 zenon_H42 zenon_He9 zenon_H2a8 zenon_H36 zenon_H9c zenon_H293 zenon_Hd4 zenon_Hc6. % 10.36/10.50 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.50 apply (zenon_L541_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.50 apply (zenon_L310_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.36/10.50 apply (zenon_L258_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.36/10.50 apply (zenon_L36_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.36/10.50 exact (zenon_H163 zenon_H103). % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.36/10.50 apply (zenon_L616_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.36/10.50 apply (zenon_L680_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.36/10.50 exact (zenon_Hff zenon_Hfc). % 10.36/10.50 apply (zenon_L219_); trivial. % 10.36/10.50 apply (zenon_L238_); trivial. % 10.36/10.50 (* end of lemma zenon_L688_ *) % 10.36/10.50 assert (zenon_L689_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H1a2 zenon_H2f zenon_H127 zenon_H2b9 zenon_H85 zenon_Hfd zenon_H12d zenon_H99 zenon_Hdf zenon_H5a zenon_Hf4 zenon_H104 zenon_Hff zenon_H290 zenon_Hda zenon_H284 zenon_Hce zenon_H2bc zenon_H163 zenon_H28f zenon_H1c9 zenon_H42 zenon_He9 zenon_H2a8 zenon_H36 zenon_H9c zenon_H293 zenon_Hd4 zenon_Hc6. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.50 exact (zenon_H2f zenon_H31). % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.50 apply (zenon_L632_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.50 apply (zenon_L421_); trivial. % 10.36/10.50 apply (zenon_L688_); trivial. % 10.36/10.50 (* end of lemma zenon_L689_ *) % 10.36/10.50 assert (zenon_L690_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((op (e0) (e0)) = (e1))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H1e1 zenon_H2f. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H127. zenon_intro zenon_H1e2. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H1e5. zenon_intro zenon_H2e. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.36/10.50 exact (zenon_H2f zenon_H31). % 10.36/10.50 (* end of lemma zenon_L690_ *) % 10.36/10.50 assert (zenon_L691_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e0)) = (e1))\/(((op (e1) (e0)) = (e2))\/((op (e1) (e0)) = (e3))))) -> (~((op (e1) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H289 zenon_H13d zenon_H303 zenon_H15b zenon_Hb6 zenon_H142 zenon_Hbb zenon_H1a2 zenon_H2b9 zenon_H85 zenon_Hfd zenon_H12d zenon_Hdf zenon_H290 zenon_Hda zenon_H284 zenon_Hce zenon_H2bc zenon_H28f zenon_He9 zenon_H2a8 zenon_H9c zenon_H293 zenon_Hc6 zenon_H302 zenon_H2ae zenon_H24b zenon_He6 zenon_H269 zenon_H15e zenon_H278 zenon_H186 zenon_H272 zenon_H94 zenon_H1a3 zenon_H244 zenon_H29d zenon_H27c zenon_H130 zenon_H17e zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H12a zenon_H2ea zenon_H1b2 zenon_H171 zenon_H2f5 zenon_He0 zenon_H182 zenon_Hc0 zenon_H298 zenon_H157 zenon_H124 zenon_H287 zenon_H191 zenon_H14b zenon_Hca zenon_Hd5 zenon_H100 zenon_H173 zenon_H115 zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H28c zenon_H135 zenon_H47 zenon_H1cb zenon_H281 zenon_H308 zenon_H104 zenon_H99 zenon_H1de zenon_H2f zenon_H163 zenon_H2ef zenon_H127 zenon_H36 zenon_Hf4. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.50 apply (zenon_L1_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.50 apply (zenon_L2_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.50 apply (zenon_L3_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.50 apply (zenon_L4_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.50 apply (zenon_L5_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.50 apply (zenon_L6_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.50 apply (zenon_L491_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.50 apply (zenon_L527_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.50 apply (zenon_L10_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.50 apply (zenon_L493_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.50 apply (zenon_L13_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H42. zenon_intro zenon_H53. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H44. zenon_intro zenon_H1c8. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.36/10.50 apply (zenon_L673_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.50 apply (zenon_L15_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.50 apply (zenon_L660_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H56. zenon_intro zenon_H62. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H58. zenon_intro zenon_H1d3. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.50 exact (zenon_H2f zenon_H31). % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.50 apply (zenon_L632_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.50 apply (zenon_L674_); trivial. % 10.36/10.50 apply (zenon_L670_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.50 apply (zenon_L19_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.50 apply (zenon_L20_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.50 apply (zenon_L21_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.50 apply (zenon_L499_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.50 apply (zenon_L500_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.50 apply (zenon_L24_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.50 apply (zenon_L25_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.50 apply (zenon_L26_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.50 apply (zenon_L27_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.50 apply (zenon_L501_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.50 apply (zenon_L31_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.50 apply (zenon_L32_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.50 apply (zenon_L502_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.50 apply (zenon_L503_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.50 apply (zenon_L56_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.50 apply (zenon_L106_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.50 apply (zenon_L147_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.50 apply (zenon_L148_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.50 apply (zenon_L671_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.50 apply (zenon_L150_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb9. zenon_intro zenon_H1b1. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H71. zenon_intro zenon_H2a. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.50 exact (zenon_H2f zenon_H31). % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.50 apply (zenon_L632_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.50 apply (zenon_L360_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.50 apply (zenon_L90_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.50 apply (zenon_L105_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.36/10.50 apply (zenon_L33_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.36/10.50 apply (zenon_L312_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.50 apply (zenon_L59_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.50 apply (zenon_L107_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.50 exact (zenon_H163 zenon_H103). % 10.36/10.50 apply (zenon_L317_); trivial. % 10.36/10.50 apply (zenon_L579_); trivial. % 10.36/10.50 apply (zenon_L633_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.50 apply (zenon_L508_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.50 apply (zenon_L634_); trivial. % 10.36/10.50 apply (zenon_L584_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.50 apply (zenon_L675_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.50 apply (zenon_L154_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.50 apply (zenon_L155_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.50 apply (zenon_L528_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.50 apply (zenon_L157_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.50 apply (zenon_L158_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.50 apply (zenon_L159_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.50 apply (zenon_L160_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_Hd4. zenon_intro zenon_H1ca. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1ca). zenon_intro zenon_Hff. zenon_intro zenon_H57. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.50 apply (zenon_L603_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.50 apply (zenon_L312_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.50 apply (zenon_L687_); trivial. % 10.36/10.50 apply (zenon_L77_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.50 apply (zenon_L604_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.50 apply (zenon_L689_); trivial. % 10.36/10.50 exact (zenon_H59 zenon_H56). % 10.36/10.50 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.50 apply (zenon_L292_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.50 apply (zenon_L164_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.50 apply (zenon_L165_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.50 apply (zenon_L166_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.50 apply (zenon_L518_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.50 apply (zenon_L529_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.50 apply (zenon_L169_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.50 apply (zenon_L690_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.50 apply (zenon_L172_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.50 apply (zenon_L577_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.50 apply (zenon_L174_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.50 apply (zenon_L531_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.50 apply (zenon_L369_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.50 apply (zenon_L178_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.50 apply (zenon_L179_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.50 apply (zenon_L180_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.50 apply (zenon_L181_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.50 apply (zenon_L182_); trivial. % 10.36/10.50 apply (zenon_L183_); trivial. % 10.36/10.50 (* end of lemma zenon_L691_ *) % 10.36/10.50 assert (zenon_L692_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.50 do 0 intro. intros zenon_H1b0 zenon_He9 zenon_H67. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb9. zenon_intro zenon_H1b1. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H71. zenon_intro zenon_H2a. % 10.36/10.50 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.36/10.50 apply (zenon_L548_); trivial. % 10.36/10.50 (* end of lemma zenon_L692_ *) % 10.36/10.50 assert (zenon_L693_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.50 do 0 intro. intros zenon_Hdf zenon_H36 zenon_Hf4 zenon_H104 zenon_Hff zenon_H290 zenon_Hda zenon_H198 zenon_H284 zenon_Hce zenon_H2bc zenon_H163 zenon_H28f zenon_H1c9 zenon_H47 zenon_H5a zenon_H2a8 zenon_H99 zenon_H9a zenon_H293 zenon_Hd4 zenon_Hc6. % 10.36/10.50 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.50 apply (zenon_L541_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.50 apply (zenon_L310_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.36/10.50 apply (zenon_L258_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.36/10.50 apply (zenon_L35_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.36/10.50 exact (zenon_H163 zenon_H103). % 10.36/10.50 apply (zenon_L681_); trivial. % 10.36/10.50 apply (zenon_L238_); trivial. % 10.36/10.50 (* end of lemma zenon_L693_ *) % 10.36/10.50 assert (zenon_L694_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H298 zenon_Hc6 zenon_H293 zenon_H9a zenon_H99 zenon_H2a8 zenon_H5a zenon_H47 zenon_H1c9 zenon_H28f zenon_H163 zenon_H2bc zenon_Hce zenon_H284 zenon_Hda zenon_H290 zenon_Hff zenon_H104 zenon_Hdf zenon_H115 zenon_H36 zenon_Hd4 zenon_Hf4 zenon_H1e5. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.36/10.50 apply (zenon_L693_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.36/10.50 apply (zenon_L65_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.36/10.50 apply (zenon_L269_); trivial. % 10.36/10.50 exact (zenon_H1e5 zenon_H189). % 10.36/10.50 (* end of lemma zenon_L694_ *) % 10.36/10.50 assert (zenon_L695_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H17e zenon_H5a zenon_H94 zenon_H104 zenon_H36 zenon_H1e5 zenon_Hf4 zenon_Hd4 zenon_H99 zenon_H290 zenon_Hda zenon_Hdb zenon_H284 zenon_Hce zenon_H2bc zenon_H163 zenon_H28f zenon_H1c9 zenon_Hff zenon_H298 zenon_Ha5 zenon_He9. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.50 apply (zenon_L359_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.50 apply (zenon_L225_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.36/10.50 apply (zenon_L680_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.36/10.50 apply (zenon_L71_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.36/10.50 apply (zenon_L269_); trivial. % 10.36/10.50 exact (zenon_H1e5 zenon_H189). % 10.36/10.50 apply (zenon_L119_); trivial. % 10.36/10.50 (* end of lemma zenon_L695_ *) % 10.36/10.50 assert (zenon_L696_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.50 do 0 intro. intros zenon_Hdf zenon_H46 zenon_He9 zenon_Ha5 zenon_H298 zenon_Hff zenon_H1c9 zenon_H28f zenon_H163 zenon_H2bc zenon_Hce zenon_H284 zenon_Hda zenon_H290 zenon_H99 zenon_Hf4 zenon_H1e5 zenon_H36 zenon_H104 zenon_H94 zenon_H5a zenon_H17e zenon_Hd4 zenon_Hc6. % 10.36/10.50 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.50 apply (zenon_L511_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.50 apply (zenon_L310_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.50 apply (zenon_L695_); trivial. % 10.36/10.50 apply (zenon_L238_); trivial. % 10.36/10.50 (* end of lemma zenon_L696_ *) % 10.36/10.50 assert (zenon_L697_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e2)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> False). % 10.36/10.50 do 0 intro. intros zenon_H17e zenon_H94 zenon_H293 zenon_H284 zenon_H9c zenon_H163 zenon_H2a8 zenon_H29d zenon_H27c zenon_He9 zenon_H186 zenon_Hfd zenon_H252 zenon_H5a zenon_H130 zenon_H244 zenon_H85 zenon_Hd4 zenon_H298 zenon_Hc6 zenon_Hda zenon_Hcd zenon_H36 zenon_Hdf zenon_H99 zenon_Hf4 zenon_H1e5 zenon_H59 zenon_H272 zenon_Hff zenon_H104. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.50 apply (zenon_L359_); trivial. % 10.36/10.50 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.51 apply (zenon_L225_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.51 apply (zenon_L550_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.36/10.51 apply (zenon_L551_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.36/10.51 apply (zenon_L36_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.36/10.51 exact (zenon_H163 zenon_H103). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.36/10.51 apply (zenon_L538_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.36/10.51 apply (zenon_L550_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.36/10.51 exact (zenon_Hff zenon_Hfc). % 10.36/10.51 apply (zenon_L219_); trivial. % 10.36/10.51 (* end of lemma zenon_L697_ *) % 10.36/10.51 assert (zenon_L698_ : (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H104 zenon_Hff zenon_H272 zenon_H59 zenon_H1e5 zenon_H99 zenon_Hdf zenon_H298 zenon_H85 zenon_H244 zenon_H130 zenon_H5a zenon_Hfd zenon_H186 zenon_He9 zenon_H27c zenon_H29d zenon_H2a8 zenon_H163 zenon_H9c zenon_H284 zenon_H293 zenon_H94 zenon_H17e zenon_H12a zenon_Hf6 zenon_H128 zenon_H177 zenon_H2b9 zenon_H36 zenon_Hf4 zenon_Hcd zenon_Hda zenon_Hd4 zenon_Hc6. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.51 apply (zenon_L89_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.51 apply (zenon_L197_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.51 apply (zenon_L279_); trivial. % 10.36/10.51 apply (zenon_L697_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.51 apply (zenon_L310_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.51 apply (zenon_L50_); trivial. % 10.36/10.51 apply (zenon_L238_); trivial. % 10.36/10.51 (* end of lemma zenon_L698_ *) % 10.36/10.51 assert (zenon_L699_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((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 (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H12d zenon_H104 zenon_Hff zenon_H272 zenon_H59 zenon_H1e5 zenon_H99 zenon_Hdf zenon_H298 zenon_H85 zenon_H244 zenon_H130 zenon_H5a zenon_Hfd zenon_H186 zenon_He9 zenon_H27c zenon_H29d zenon_H2a8 zenon_H163 zenon_H9c zenon_H284 zenon_H293 zenon_H94 zenon_H17e zenon_H12a zenon_Hf6 zenon_H177 zenon_H2b9 zenon_H36 zenon_Hf4 zenon_Hcd zenon_Hda zenon_Hd4 zenon_Hc6. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.51 apply (zenon_L58_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.51 apply (zenon_L312_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.51 apply (zenon_L89_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.51 apply (zenon_L197_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.51 apply (zenon_L45_); trivial. % 10.36/10.51 apply (zenon_L697_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.51 apply (zenon_L310_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.51 apply (zenon_L50_); trivial. % 10.36/10.51 apply (zenon_L238_); trivial. % 10.36/10.51 apply (zenon_L698_); trivial. % 10.36/10.51 (* end of lemma zenon_L699_ *) % 10.36/10.51 assert (zenon_L700_ : (~((op (e2) (op (e2) (e2))) = (op (e2) (e0)))) -> ((op (e2) (e2)) = (e0)) -> False). % 10.36/10.51 do 0 intro. intros zenon_H30b zenon_H74. % 10.36/10.51 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 10.36/10.51 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.36/10.51 congruence. % 10.36/10.51 apply zenon_H87. apply refl_equal. % 10.36/10.51 exact (zenon_H71 zenon_H74). % 10.36/10.51 (* end of lemma zenon_L700_ *) % 10.36/10.51 assert (zenon_L701_ : ((op (e1) (e2)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> (~((e3) = (op (op (e2) (op (e2) (e2))) (e2)))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H17a zenon_Hfa zenon_H74 zenon_H164. % 10.36/10.51 elim (classic ((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 10.36/10.51 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2))) = ((e3) = (op (op (e2) (op (e2) (e2))) (e2)))). % 10.36/10.51 intro zenon_D_pnotp. % 10.36/10.51 apply zenon_H164. % 10.36/10.51 rewrite <- zenon_D_pnotp. % 10.36/10.51 exact zenon_H110. % 10.36/10.51 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 10.36/10.51 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 10.36/10.51 congruence. % 10.36/10.51 cut (((op (e1) (e2)) = (e3)) = ((op (op (e2) (op (e2) (e2))) (e2)) = (e3))). % 10.36/10.51 intro zenon_D_pnotp. % 10.36/10.51 apply zenon_H165. % 10.36/10.51 rewrite <- zenon_D_pnotp. % 10.36/10.51 exact zenon_H17a. % 10.36/10.51 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.36/10.51 cut (((op (e1) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 10.36/10.51 congruence. % 10.36/10.51 elim (classic ((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 10.36/10.51 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2))) = ((op (e1) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))). % 10.36/10.51 intro zenon_D_pnotp. % 10.36/10.51 apply zenon_H113. % 10.36/10.51 rewrite <- zenon_D_pnotp. % 10.36/10.51 exact zenon_H110. % 10.36/10.51 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (op (e2) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 10.36/10.51 cut (((op (op (e2) (op (e2) (e2))) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 10.36/10.51 congruence. % 10.36/10.51 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.36/10.51 cut (((op (e2) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 10.36/10.51 congruence. % 10.36/10.51 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (op (e2) (e2))) = (e1))). % 10.36/10.51 intro zenon_D_pnotp. % 10.36/10.51 apply zenon_H10e. % 10.36/10.51 rewrite <- zenon_D_pnotp. % 10.36/10.51 exact zenon_Hfa. % 10.36/10.51 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.36/10.51 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H30c]. % 10.36/10.51 congruence. % 10.36/10.51 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.36/10.51 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e0)) = (op (e2) (op (e2) (e2))))). % 10.36/10.51 intro zenon_D_pnotp. % 10.36/10.51 apply zenon_H30c. % 10.36/10.51 rewrite <- zenon_D_pnotp. % 10.36/10.51 exact zenon_H10c. % 10.36/10.51 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.36/10.51 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H30b]. % 10.36/10.51 congruence. % 10.36/10.51 apply (zenon_L700_); trivial. % 10.36/10.51 apply zenon_H10d. apply refl_equal. % 10.36/10.51 apply zenon_H10d. apply refl_equal. % 10.36/10.51 apply zenon_H98. apply refl_equal. % 10.36/10.51 apply zenon_H87. apply refl_equal. % 10.36/10.51 apply zenon_H111. apply refl_equal. % 10.36/10.51 apply zenon_H111. apply refl_equal. % 10.36/10.51 apply zenon_Heb. apply refl_equal. % 10.36/10.51 apply zenon_H111. apply refl_equal. % 10.36/10.51 apply zenon_H111. apply refl_equal. % 10.36/10.51 (* end of lemma zenon_L701_ *) % 10.36/10.51 assert (zenon_L702_ : ((op (e1) (e2)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> False). % 10.36/10.51 do 0 intro. intros zenon_H17a zenon_Hfa zenon_H74. % 10.36/10.51 apply (zenon_notand_s _ _ ax18); [ zenon_intro zenon_H301 | zenon_intro zenon_H30d ]. % 10.36/10.51 apply zenon_H301. apply sym_equal. exact zenon_H74. % 10.36/10.51 apply (zenon_notand_s _ _ zenon_H30d); [ zenon_intro zenon_H10b | zenon_intro zenon_H164 ]. % 10.36/10.51 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.36/10.51 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((e1) = (op (e2) (op (e2) (e2))))). % 10.36/10.51 intro zenon_D_pnotp. % 10.36/10.51 apply zenon_H10b. % 10.36/10.51 rewrite <- zenon_D_pnotp. % 10.36/10.51 exact zenon_H10c. % 10.36/10.51 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.36/10.51 cut (((op (e2) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 10.36/10.51 congruence. % 10.36/10.51 cut (((op (e2) (e0)) = (e1)) = ((op (e2) (op (e2) (e2))) = (e1))). % 10.36/10.51 intro zenon_D_pnotp. % 10.36/10.51 apply zenon_H10e. % 10.36/10.51 rewrite <- zenon_D_pnotp. % 10.36/10.51 exact zenon_Hfa. % 10.36/10.51 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.36/10.51 cut (((op (e2) (e0)) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H30c]. % 10.36/10.51 congruence. % 10.36/10.51 elim (classic ((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [ zenon_intro zenon_H10c | zenon_intro zenon_H10d ]. % 10.36/10.51 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2)))) = ((op (e2) (e0)) = (op (e2) (op (e2) (e2))))). % 10.36/10.51 intro zenon_D_pnotp. % 10.36/10.51 apply zenon_H30c. % 10.36/10.51 rewrite <- zenon_D_pnotp. % 10.36/10.51 exact zenon_H10c. % 10.36/10.51 cut (((op (e2) (op (e2) (e2))) = (op (e2) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 10.36/10.51 cut (((op (e2) (op (e2) (e2))) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H30b]. % 10.36/10.51 congruence. % 10.36/10.51 apply (zenon_L700_); trivial. % 10.36/10.51 apply zenon_H10d. apply refl_equal. % 10.36/10.51 apply zenon_H10d. apply refl_equal. % 10.36/10.51 apply zenon_H98. apply refl_equal. % 10.36/10.51 apply zenon_H10d. apply refl_equal. % 10.36/10.51 apply zenon_H10d. apply refl_equal. % 10.36/10.51 apply (zenon_L701_); trivial. % 10.36/10.51 (* end of lemma zenon_L702_ *) % 10.36/10.51 assert (zenon_L703_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 10.36/10.51 do 0 intro. intros zenon_H124 zenon_H74 zenon_H17a zenon_H36 zenon_H171 zenon_H163 zenon_Hf4 zenon_Hd4. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.51 apply (zenon_L702_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.51 apply (zenon_L107_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.51 exact (zenon_H163 zenon_H103). % 10.36/10.51 apply (zenon_L269_); trivial. % 10.36/10.51 (* end of lemma zenon_L703_ *) % 10.36/10.51 assert (zenon_L704_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H17e zenon_H5a zenon_H94 zenon_H104 zenon_H36 zenon_Hff zenon_H1c9 zenon_H28f zenon_H163 zenon_H2bc zenon_Hce zenon_H284 zenon_H198 zenon_Hdb zenon_Hda zenon_H290 zenon_Ha5 zenon_He9. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.51 apply (zenon_L359_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.51 apply (zenon_L225_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.51 apply (zenon_L680_); trivial. % 10.36/10.51 apply (zenon_L119_); trivial. % 10.36/10.51 (* end of lemma zenon_L704_ *) % 10.36/10.51 assert (zenon_L705_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.51 do 0 intro. intros zenon_Hdf zenon_Hf4 zenon_He9 zenon_Ha5 zenon_H290 zenon_Hda zenon_H198 zenon_H284 zenon_Hce zenon_H2bc zenon_H163 zenon_H28f zenon_H1c9 zenon_Hff zenon_H36 zenon_H104 zenon_H94 zenon_H5a zenon_H17e zenon_Hd4 zenon_Hc6. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.51 apply (zenon_L541_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.51 apply (zenon_L310_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.51 apply (zenon_L704_); trivial. % 10.36/10.51 apply (zenon_L238_); trivial. % 10.36/10.51 (* end of lemma zenon_L705_ *) % 10.36/10.51 assert (zenon_L706_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H272 zenon_H59 zenon_H298 zenon_Hff zenon_H1c9 zenon_H28f zenon_H163 zenon_H2bc zenon_Hce zenon_H284 zenon_Hdb zenon_Hda zenon_H290 zenon_H99 zenon_Hf4 zenon_H1e5 zenon_H36 zenon_H104 zenon_H94 zenon_H17e zenon_Hd4 zenon_H85 zenon_H244 zenon_H130 zenon_H5a zenon_H252 zenon_Hfd zenon_H186 zenon_H17a zenon_He9. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.36/10.51 exact (zenon_H59 zenon_H56). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.36/10.51 apply (zenon_L695_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.36/10.51 apply (zenon_L234_); trivial. % 10.36/10.51 apply (zenon_L549_); trivial. % 10.36/10.51 (* end of lemma zenon_L706_ *) % 10.36/10.51 assert (zenon_L707_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> ((op (e2) (e0)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.36/10.51 do 0 intro. intros zenon_He0 zenon_Hfa zenon_H252 zenon_H154 zenon_H182 zenon_Hdb zenon_H298 zenon_H284 zenon_H16e zenon_H104 zenon_H17c zenon_Hf4 zenon_H1e5. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.36/10.51 apply (zenon_L59_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.36/10.51 apply (zenon_L333_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.36/10.51 apply (zenon_L307_); trivial. % 10.36/10.51 apply (zenon_L551_); trivial. % 10.36/10.51 (* end of lemma zenon_L707_ *) % 10.36/10.51 assert (zenon_L708_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H12a zenon_Hdb zenon_H182 zenon_H46 zenon_Hc0 zenon_He0 zenon_H100 zenon_Hf6 zenon_H154 zenon_H29d zenon_H27c zenon_H186 zenon_H252 zenon_H130 zenon_H244 zenon_H17e zenon_H94 zenon_H1e5 zenon_H298 zenon_H59 zenon_H272 zenon_H124 zenon_H1a2 zenon_H2f zenon_H2b9 zenon_H85 zenon_Hfd zenon_H12d zenon_H99 zenon_Hdf zenon_H5a zenon_Hf4 zenon_H104 zenon_Hff zenon_H290 zenon_Hda zenon_H284 zenon_Hce zenon_H2bc zenon_H163 zenon_H28f zenon_H1c9 zenon_H42 zenon_He9 zenon_H2a8 zenon_H36 zenon_H9c zenon_H293 zenon_Hd4 zenon_Hc6. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.51 apply (zenon_L359_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.51 apply (zenon_L225_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.51 apply (zenon_L706_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.51 apply (zenon_L99_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.51 apply (zenon_L225_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.36/10.51 apply (zenon_L707_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.36/10.51 apply (zenon_L36_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.36/10.51 exact (zenon_H163 zenon_H103). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.36/10.51 apply (zenon_L538_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.36/10.51 apply (zenon_L706_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.36/10.51 exact (zenon_Hff zenon_Hfc). % 10.36/10.51 apply (zenon_L219_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.51 apply (zenon_L61_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.51 exact (zenon_H163 zenon_H103). % 10.36/10.51 apply (zenon_L544_); trivial. % 10.36/10.51 apply (zenon_L689_); trivial. % 10.36/10.51 (* end of lemma zenon_L708_ *) % 10.36/10.51 assert (zenon_L709_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H293 zenon_H9c zenon_H36 zenon_H2a8 zenon_He9 zenon_H42 zenon_H1c9 zenon_H28f zenon_H163 zenon_H2bc zenon_Hce zenon_H284 zenon_Hda zenon_H290 zenon_Hff zenon_H104 zenon_Hf4 zenon_H5a zenon_Hdf zenon_H99 zenon_H12d zenon_Hfd zenon_H85 zenon_H2b9 zenon_H2f zenon_H1a2 zenon_H124 zenon_H272 zenon_H59 zenon_H298 zenon_H1e5 zenon_H94 zenon_H17e zenon_H244 zenon_H130 zenon_H186 zenon_H27c zenon_H29d zenon_H154 zenon_Hf6 zenon_H100 zenon_He0 zenon_Hc0 zenon_H46 zenon_H182 zenon_H12a zenon_H128 zenon_Hd4 zenon_Hc6. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.51 apply (zenon_L511_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.51 apply (zenon_L310_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.51 apply (zenon_L89_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.51 apply (zenon_L310_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.51 apply (zenon_L279_); trivial. % 10.36/10.51 apply (zenon_L708_); trivial. % 10.36/10.51 apply (zenon_L238_); trivial. % 10.36/10.51 (* end of lemma zenon_L709_ *) % 10.36/10.51 assert (zenon_L710_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H1da zenon_H51 zenon_H85. % 10.36/10.51 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_H13b. zenon_intro zenon_H1db. % 10.36/10.51 apply (zenon_and_s _ _ zenon_H1db). zenon_intro zenon_H76. zenon_intro zenon_H27. % 10.36/10.51 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.36/10.51 apply (zenon_L595_); trivial. % 10.36/10.51 (* end of lemma zenon_L710_ *) % 10.36/10.51 assert (zenon_L711_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H272 zenon_H99 zenon_H198 zenon_He9 zenon_H17c zenon_H74 zenon_H28f zenon_H76. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.36/10.51 apply (zenon_L670_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.36/10.51 apply (zenon_L119_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.36/10.51 apply (zenon_L412_); trivial. % 10.36/10.51 exact (zenon_H76 zenon_H79). % 10.36/10.51 (* end of lemma zenon_L711_ *) % 10.36/10.51 assert (zenon_L712_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 10.36/10.51 do 0 intro. intros zenon_He0 zenon_H73 zenon_Hfd zenon_H120 zenon_H85 zenon_H1da zenon_H298 zenon_H76 zenon_H28f zenon_H74 zenon_He9 zenon_H99 zenon_H272 zenon_H104 zenon_H17c zenon_Hf4 zenon_H1e5. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.36/10.51 exact (zenon_H73 zenon_Hb9). % 10.36/10.51 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.36/10.51 apply (zenon_L73_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.36/10.51 apply (zenon_L710_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.36/10.51 apply (zenon_L711_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.36/10.51 apply (zenon_L341_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.36/10.51 apply (zenon_L269_); trivial. % 10.36/10.51 exact (zenon_H1e5 zenon_H189). % 10.36/10.51 (* end of lemma zenon_L712_ *) % 10.36/10.51 assert (zenon_L713_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H17e zenon_H13d zenon_H13b zenon_Hfa zenon_H12a zenon_H1e5 zenon_H104 zenon_H272 zenon_H99 zenon_He9 zenon_H74 zenon_H28f zenon_H76 zenon_H298 zenon_H1da zenon_H73 zenon_He0 zenon_H2b9 zenon_Hf6 zenon_H36 zenon_Hf4 zenon_Hc4 zenon_H85 zenon_Hfd. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.51 apply (zenon_L85_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.51 apply (zenon_L225_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.51 apply (zenon_L702_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.51 apply (zenon_L99_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.51 apply (zenon_L225_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.51 apply (zenon_L712_); trivial. % 10.36/10.51 apply (zenon_L623_); trivial. % 10.36/10.51 (* end of lemma zenon_L713_ *) % 10.36/10.51 assert (zenon_L714_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e2) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (e2))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> False). % 10.36/10.51 do 0 intro. intros zenon_H12a zenon_Hf6 zenon_H36 zenon_H1e5 zenon_Hf4 zenon_H17c zenon_H104 zenon_H272 zenon_H99 zenon_H74 zenon_H28f zenon_H76 zenon_H298 zenon_H1da zenon_H85 zenon_Hfd zenon_H73 zenon_He0 zenon_He9 zenon_H128. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.51 apply (zenon_L99_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.51 apply (zenon_L225_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.51 apply (zenon_L712_); trivial. % 10.36/10.51 apply (zenon_L77_); trivial. % 10.36/10.51 (* end of lemma zenon_L714_ *) % 10.36/10.51 assert (zenon_L715_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.36/10.51 do 0 intro. intros zenon_H191 zenon_H2f zenon_H177 zenon_H76 zenon_H28f zenon_H74 zenon_He9 zenon_H198 zenon_H99 zenon_H272 zenon_H36 zenon_H13d zenon_H17e zenon_H104 zenon_H13b. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.51 exact (zenon_H2f zenon_H31). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.51 apply (zenon_L282_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.51 apply (zenon_L85_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.51 apply (zenon_L225_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.51 apply (zenon_L702_); trivial. % 10.36/10.51 apply (zenon_L711_); trivial. % 10.36/10.51 apply (zenon_L123_); trivial. % 10.36/10.51 (* end of lemma zenon_L715_ *) % 10.36/10.51 assert (zenon_L716_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.36/10.51 do 0 intro. intros zenon_H293 zenon_H46 zenon_H13c zenon_H9c zenon_H36 zenon_H163 zenon_H104 zenon_H1ed. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.36/10.51 apply (zenon_L556_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.36/10.51 apply (zenon_L36_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.36/10.51 exact (zenon_H163 zenon_H103). % 10.36/10.51 apply (zenon_L219_); trivial. % 10.36/10.51 (* end of lemma zenon_L716_ *) % 10.36/10.51 assert (zenon_L717_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.36/10.51 do 0 intro. intros zenon_H293 zenon_H1e5 zenon_Hf4 zenon_H17c zenon_H284 zenon_H298 zenon_Hdb zenon_H182 zenon_H154 zenon_H252 zenon_Hfa zenon_He0 zenon_H9c zenon_H36 zenon_H163 zenon_H104 zenon_H1ed. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.36/10.51 apply (zenon_L707_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.36/10.51 apply (zenon_L36_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.36/10.51 exact (zenon_H163 zenon_H103). % 10.36/10.51 apply (zenon_L219_); trivial. % 10.36/10.51 (* end of lemma zenon_L717_ *) % 10.36/10.51 assert (zenon_L718_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.36/10.51 do 0 intro. intros zenon_H12d zenon_H2e7 zenon_H56 zenon_H99 zenon_H36 zenon_Hc3 zenon_H85 zenon_He9 zenon_H127. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.51 apply (zenon_L496_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.51 apply (zenon_L312_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.51 apply (zenon_L45_); trivial. % 10.36/10.51 apply (zenon_L77_); trivial. % 10.36/10.51 (* end of lemma zenon_L718_ *) % 10.36/10.51 assert (zenon_L719_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H12a zenon_Hf6 zenon_H104 zenon_Hfd zenon_H12d zenon_H2e7 zenon_H56 zenon_H99 zenon_H36 zenon_Hc3 zenon_H85 zenon_He9. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.51 apply (zenon_L99_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.51 apply (zenon_L225_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.51 apply (zenon_L73_); trivial. % 10.36/10.51 apply (zenon_L718_); trivial. % 10.36/10.51 (* end of lemma zenon_L719_ *) % 10.36/10.51 assert (zenon_L720_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e2) (e2)) = (e3)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.36/10.51 do 0 intro. intros zenon_Hca zenon_H152 zenon_Hc3 zenon_H85 zenon_He9 zenon_Hfc zenon_H157 zenon_H56. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.36/10.51 apply (zenon_L658_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.36/10.51 apply (zenon_L45_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.36/10.51 apply (zenon_L319_); trivial. % 10.36/10.51 apply (zenon_L209_); trivial. % 10.36/10.51 (* end of lemma zenon_L720_ *) % 10.36/10.51 assert (zenon_L721_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H303 zenon_H5b zenon_H56 zenon_H2f zenon_Hba zenon_H94 zenon_H13b zenon_H130. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H1f | zenon_intro zenon_H304 ]. % 10.36/10.51 apply (zenon_L16_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H31 | zenon_intro zenon_H305 ]. % 10.36/10.51 exact (zenon_H2f zenon_H31). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H46 | zenon_intro zenon_H5a ]. % 10.36/10.51 apply (zenon_L511_); trivial. % 10.36/10.51 apply (zenon_L133_); trivial. % 10.36/10.51 (* end of lemma zenon_L721_ *) % 10.36/10.51 assert (zenon_L722_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H289 zenon_H58 zenon_H16e zenon_H157 zenon_Hfc zenon_He9 zenon_H85 zenon_Hc3 zenon_Hca zenon_H303 zenon_H5b zenon_H56 zenon_H2f zenon_Hba zenon_H94 zenon_H130. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.51 exact (zenon_H58 zenon_H5a). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.51 apply (zenon_L665_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.51 apply (zenon_L720_); trivial. % 10.36/10.51 apply (zenon_L721_); trivial. % 10.36/10.51 (* end of lemma zenon_L722_ *) % 10.36/10.51 assert (zenon_L723_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e2)) -> False). % 10.36/10.51 do 0 intro. intros zenon_H289 zenon_H58 zenon_H16e zenon_H2f zenon_H5b zenon_H303 zenon_H56 zenon_H157 zenon_Hfc zenon_He9 zenon_H85 zenon_Hc3 zenon_Hca zenon_Hfd zenon_H136. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.51 exact (zenon_H58 zenon_H5a). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.51 apply (zenon_L665_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.51 apply (zenon_L720_); trivial. % 10.36/10.51 apply (zenon_L255_); trivial. % 10.36/10.51 (* end of lemma zenon_L723_ *) % 10.36/10.51 assert (zenon_L724_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H281 zenon_H1e5 zenon_H27c zenon_H262 zenon_H36 zenon_H104 zenon_H18a zenon_H130 zenon_H94 zenon_Hfa zenon_Hf4 zenon_H289 zenon_H58 zenon_H16e zenon_H2f zenon_H5b zenon_H303 zenon_H56 zenon_H157 zenon_Hfc zenon_He9 zenon_H85 zenon_Hc3 zenon_Hca zenon_Hfd. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.51 exact (zenon_H58 zenon_H5a). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.51 apply (zenon_L556_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.51 apply (zenon_L720_); trivial. % 10.36/10.51 apply (zenon_L669_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.51 apply (zenon_L722_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.51 apply (zenon_L59_); trivial. % 10.36/10.51 apply (zenon_L723_); trivial. % 10.36/10.51 (* end of lemma zenon_L724_ *) % 10.36/10.51 assert (zenon_L725_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H289 zenon_H58 zenon_H16e zenon_He9 zenon_Hc1 zenon_H303 zenon_H5b zenon_H56 zenon_H2f zenon_Hba zenon_H94 zenon_H130. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.51 exact (zenon_H58 zenon_H5a). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.51 apply (zenon_L665_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.51 apply (zenon_L658_); trivial. % 10.36/10.51 apply (zenon_L721_); trivial. % 10.36/10.51 (* end of lemma zenon_L725_ *) % 10.36/10.51 assert (zenon_L726_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> False). % 10.36/10.51 do 0 intro. intros zenon_H130 zenon_H46 zenon_H136. % 10.36/10.51 cut (((op (e0) (e0)) = (e2)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 10.36/10.51 intro zenon_D_pnotp. % 10.36/10.51 apply zenon_H130. % 10.36/10.51 rewrite <- zenon_D_pnotp. % 10.36/10.51 exact zenon_H46. % 10.36/10.51 cut (((e2) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 10.36/10.51 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 10.36/10.51 congruence. % 10.36/10.51 apply zenon_H97. apply refl_equal. % 10.36/10.51 apply zenon_H137. apply sym_equal. exact zenon_H136. % 10.36/10.51 (* end of lemma zenon_L726_ *) % 10.36/10.51 assert (zenon_L727_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H303 zenon_Hc1 zenon_Hc0 zenon_H2f zenon_H136 zenon_H130 zenon_H58. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H1f | zenon_intro zenon_H304 ]. % 10.36/10.51 apply (zenon_L44_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H31 | zenon_intro zenon_H305 ]. % 10.36/10.51 exact (zenon_H2f zenon_H31). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H46 | zenon_intro zenon_H5a ]. % 10.36/10.51 apply (zenon_L726_); trivial. % 10.36/10.51 exact (zenon_H58 zenon_H5a). % 10.36/10.51 (* end of lemma zenon_L727_ *) % 10.36/10.51 assert (zenon_L728_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e1)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.36/10.51 do 0 intro. intros zenon_H191 zenon_H177 zenon_Hf4 zenon_H18a zenon_H36 zenon_H262 zenon_H27c zenon_H1e5 zenon_H281 zenon_H104 zenon_H94 zenon_H56 zenon_H5b zenon_He9 zenon_H16e zenon_H289 zenon_H85 zenon_H303 zenon_Hc1 zenon_Hc0 zenon_H2f zenon_H130 zenon_H58. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.51 exact (zenon_H2f zenon_H31). % 10.36/10.51 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.51 apply (zenon_L282_); trivial. % 10.36/10.51 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.52 exact (zenon_H58 zenon_H5a). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.52 apply (zenon_L556_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.52 apply (zenon_L658_); trivial. % 10.36/10.52 apply (zenon_L669_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.52 apply (zenon_L725_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.52 apply (zenon_L59_); trivial. % 10.36/10.52 apply (zenon_L727_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.52 exact (zenon_H58 zenon_H5a). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.52 apply (zenon_L556_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.52 apply (zenon_L658_); trivial. % 10.36/10.52 apply (zenon_L123_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.52 apply (zenon_L725_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.52 apply (zenon_L417_); trivial. % 10.36/10.52 apply (zenon_L727_); trivial. % 10.36/10.52 (* end of lemma zenon_L728_ *) % 10.36/10.52 assert (zenon_L729_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H12a zenon_Hf6 zenon_H104 zenon_H36 zenon_Hfd zenon_Hc3 zenon_H1da zenon_H1de. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.52 apply (zenon_L99_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.52 apply (zenon_L225_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.52 apply (zenon_L73_); trivial. % 10.36/10.52 apply (zenon_L529_); trivial. % 10.36/10.52 (* end of lemma zenon_L729_ *) % 10.36/10.52 assert (zenon_L730_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (e0))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e3)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H12d zenon_He6 zenon_Hd5 zenon_H24b zenon_H16e zenon_H284 zenon_H157 zenon_H269 zenon_He0 zenon_Hc0 zenon_H46 zenon_H2ef zenon_H1de zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H171 zenon_H202 zenon_H154 zenon_H262 zenon_H2f2 zenon_He9 zenon_H26e zenon_H245 zenon_H298 zenon_H104 zenon_Hf4 zenon_H2ae zenon_H45 zenon_H293 zenon_H1ed zenon_H191 zenon_H29d zenon_H272 zenon_H15e zenon_H287 zenon_Hc6 zenon_H2b9 zenon_H12a zenon_H2f5 zenon_Hfd zenon_H94 zenon_H182 zenon_Hdf zenon_H17e zenon_H186 zenon_Hca zenon_H5a zenon_H99 zenon_H36 zenon_Hc3 zenon_H85 zenon_H2cf zenon_H2ed zenon_H1e5 zenon_H1ee zenon_H1eb zenon_H2cd. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.52 apply (zenon_L597_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.52 apply (zenon_L312_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.52 apply (zenon_L45_); trivial. % 10.36/10.52 apply (zenon_L526_); trivial. % 10.36/10.52 (* end of lemma zenon_L730_ *) % 10.36/10.52 assert (zenon_L731_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H12d zenon_He9 zenon_H119 zenon_H99 zenon_H36 zenon_Hc3 zenon_H85 zenon_H2cf zenon_H2ed zenon_H1e5 zenon_H1ee zenon_H1eb zenon_H2cd. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.52 apply (zenon_L134_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.52 apply (zenon_L312_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.52 apply (zenon_L45_); trivial. % 10.36/10.52 apply (zenon_L526_); trivial. % 10.36/10.52 (* end of lemma zenon_L731_ *) % 10.36/10.52 assert (zenon_L732_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H2bc zenon_H45 zenon_H103 zenon_Hce zenon_H2d9 zenon_H1ed zenon_H27c. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H42 | zenon_intro zenon_H2bd ]. % 10.36/10.52 exact (zenon_H45 zenon_H42). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H16e | zenon_intro zenon_H2be ]. % 10.36/10.52 apply (zenon_L366_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_Hcd | zenon_intro zenon_H150 ]. % 10.36/10.52 apply (zenon_L401_); trivial. % 10.36/10.52 apply (zenon_L252_); trivial. % 10.36/10.52 (* end of lemma zenon_L732_ *) % 10.36/10.52 assert (zenon_L733_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 10.36/10.52 do 0 intro. intros zenon_H124 zenon_H104 zenon_H287 zenon_H36 zenon_H9c zenon_H284 zenon_H293 zenon_Hf4 zenon_H1ee zenon_H2bc zenon_H45 zenon_Hce zenon_H1ed zenon_H27c zenon_H154 zenon_Hc3 zenon_H130 zenon_H46 zenon_H2db zenon_H157 zenon_H198. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.52 apply (zenon_L557_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.52 apply (zenon_L193_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H136 | zenon_intro zenon_H2dc ]. % 10.36/10.52 apply (zenon_L726_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H252 | zenon_intro zenon_H2dd ]. % 10.36/10.52 apply (zenon_L333_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H2d9 | zenon_intro zenon_Hd3 ]. % 10.36/10.52 apply (zenon_L732_); trivial. % 10.36/10.52 exact (zenon_H1ee zenon_Hd3). % 10.36/10.52 apply (zenon_L210_); trivial. % 10.36/10.52 (* end of lemma zenon_L733_ *) % 10.36/10.52 assert (zenon_L734_ : ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 10.36/10.52 do 0 intro. intros zenon_Hc3 zenon_H171 zenon_H47 zenon_H1a2 zenon_H1a3 zenon_H15e zenon_H244 zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H1de zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H2f5 zenon_Hf4 zenon_H13d zenon_H14b zenon_H135 zenon_H303 zenon_H130 zenon_H289 zenon_H281 zenon_H100 zenon_H191 zenon_H99 zenon_H36 zenon_H85 zenon_H12a zenon_He9 zenon_Hfd zenon_H104 zenon_H12d zenon_H2f zenon_Hc0 zenon_H30e zenon_H5b zenon_H94 zenon_Hca zenon_H157 zenon_H18a zenon_H27c zenon_H272 zenon_H28f zenon_H17e zenon_Hdf zenon_H2ae zenon_H287 zenon_H24b zenon_He6 zenon_Hd5 zenon_H269 zenon_H29d zenon_H293 zenon_Hc6 zenon_H186 zenon_He0 zenon_H284 zenon_H298 zenon_H182 zenon_H124 zenon_H2bc zenon_Hce zenon_H2db. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H127 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.52 apply (zenon_L1_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.52 apply (zenon_L2_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.52 apply (zenon_L3_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.52 apply (zenon_L4_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.52 apply (zenon_L5_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.52 apply (zenon_L6_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.52 apply (zenon_L512_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.52 apply (zenon_L492_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.52 apply (zenon_L10_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.52 apply (zenon_L513_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.52 apply (zenon_L13_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H42. zenon_intro zenon_H53. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H44. zenon_intro zenon_H1c8. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H1f | zenon_intro zenon_H30f ]. % 10.36/10.52 apply (zenon_L11_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H95 | zenon_intro zenon_H310 ]. % 10.36/10.52 apply (zenon_L618_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H131 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.52 exact (zenon_H2f zenon_H31). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.52 apply (zenon_L605_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.52 apply (zenon_L421_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.52 exact (zenon_H44 zenon_H46). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.52 apply (zenon_L541_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.52 apply (zenon_L608_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.52 apply (zenon_L658_); trivial. % 10.36/10.52 apply (zenon_L659_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.52 apply (zenon_L417_); trivial. % 10.36/10.52 apply (zenon_L656_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.52 apply (zenon_L494_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.52 apply (zenon_L312_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.52 apply (zenon_L45_); trivial. % 10.36/10.52 apply (zenon_L220_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.52 apply (zenon_L15_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.52 apply (zenon_L660_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H56. zenon_intro zenon_H62. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H58. zenon_intro zenon_H1d3. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H1f | zenon_intro zenon_H30f ]. % 10.36/10.52 apply (zenon_L16_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H95 | zenon_intro zenon_H310 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.52 exact (zenon_H2f zenon_H31). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.52 apply (zenon_L719_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.52 exact (zenon_H2f zenon_H31). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.52 apply (zenon_L394_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.52 apply (zenon_L724_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.52 exact (zenon_H58 zenon_H5a). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.52 apply (zenon_L665_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.52 apply (zenon_L720_); trivial. % 10.36/10.52 apply (zenon_L123_); trivial. % 10.36/10.52 apply (zenon_L670_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H131 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.52 exact (zenon_H2f zenon_H31). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.52 apply (zenon_L719_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.52 apply (zenon_L728_); trivial. % 10.36/10.52 apply (zenon_L670_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.52 apply (zenon_L496_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.52 apply (zenon_L312_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.52 apply (zenon_L45_); trivial. % 10.36/10.52 apply (zenon_L220_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.52 apply (zenon_L19_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.52 apply (zenon_L20_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.52 apply (zenon_L21_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.52 apply (zenon_L499_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.52 apply (zenon_L500_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.52 apply (zenon_L24_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.52 apply (zenon_L25_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.52 apply (zenon_L26_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.52 apply (zenon_L27_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.52 apply (zenon_L501_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.52 apply (zenon_L31_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.52 apply (zenon_L32_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.52 apply (zenon_L502_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.52 apply (zenon_L503_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.52 apply (zenon_L56_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.52 apply (zenon_L106_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.52 apply (zenon_L147_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.52 apply (zenon_L148_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.52 apply (zenon_L671_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.52 apply (zenon_L150_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.52 apply (zenon_L514_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.52 apply (zenon_L675_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.52 apply (zenon_L154_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.52 apply (zenon_L155_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.52 apply (zenon_L510_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.52 apply (zenon_L157_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.52 apply (zenon_L158_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.52 apply (zenon_L159_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.52 apply (zenon_L160_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.52 apply (zenon_L516_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.52 apply (zenon_L292_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.52 apply (zenon_L164_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.52 apply (zenon_L165_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.52 apply (zenon_L166_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.52 apply (zenon_L518_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_H13b. zenon_intro zenon_H1db. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H1db). zenon_intro zenon_H76. zenon_intro zenon_H27. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.52 exact (zenon_H2f zenon_H31). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.52 apply (zenon_L729_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.52 apply (zenon_L669_); trivial. % 10.36/10.52 apply (zenon_L715_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.52 apply (zenon_L169_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.52 apply (zenon_L690_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.52 apply (zenon_L172_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.52 apply (zenon_L521_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.52 apply (zenon_L174_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ed. zenon_intro zenon_H1ec. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ee. zenon_intro zenon_H43. % 10.36/10.52 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.52 exact (zenon_H2f zenon_H31). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.52 apply (zenon_L58_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.52 apply (zenon_L312_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.52 apply (zenon_L45_); trivial. % 10.36/10.52 apply (zenon_L526_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.52 apply (zenon_L730_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.52 apply (zenon_L731_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.52 apply (zenon_L252_); trivial. % 10.36/10.52 apply (zenon_L592_); trivial. % 10.36/10.52 apply (zenon_L733_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.52 apply (zenon_L369_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.52 apply (zenon_L178_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.52 apply (zenon_L179_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.52 apply (zenon_L180_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.52 apply (zenon_L181_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.52 apply (zenon_L182_); trivial. % 10.36/10.52 apply (zenon_L183_); trivial. % 10.36/10.52 apply (zenon_L606_); trivial. % 10.36/10.52 (* end of lemma zenon_L734_ *) % 10.36/10.52 assert (zenon_L735_ : ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e1)) -> False). % 10.36/10.52 do 0 intro. intros zenon_H46 zenon_H2db zenon_Hce zenon_H2bc zenon_H124 zenon_H298 zenon_H284 zenon_He0 zenon_H186 zenon_Hc6 zenon_H293 zenon_H29d zenon_H269 zenon_Hd5 zenon_He6 zenon_H24b zenon_H287 zenon_H2ae zenon_Hdf zenon_H17e zenon_H28f zenon_H272 zenon_H27c zenon_H18a zenon_H157 zenon_Hca zenon_H94 zenon_H5b zenon_H30e zenon_Hc0 zenon_H2f zenon_H12d zenon_H104 zenon_Hfd zenon_He9 zenon_H12a zenon_H85 zenon_H36 zenon_H99 zenon_H191 zenon_H100 zenon_H281 zenon_H289 zenon_H130 zenon_H303 zenon_H135 zenon_H14b zenon_H13d zenon_H2f5 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H1de zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_H244 zenon_H15e zenon_H1a3 zenon_H1a2 zenon_H47 zenon_H171 zenon_H182 zenon_Hdb zenon_Hf4 zenon_H107. % 10.36/10.52 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.36/10.52 apply (zenon_L88_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.36/10.52 apply (zenon_L734_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.36/10.52 apply (zenon_L307_); trivial. % 10.36/10.52 apply (zenon_L269_); trivial. % 10.36/10.52 (* end of lemma zenon_L735_ *) % 10.36/10.52 assert (zenon_L736_ : ((op (e3) (e2)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H1ed zenon_H252 zenon_H17c zenon_H1e5 zenon_Hf6 zenon_H163 zenon_H46 zenon_H2db zenon_Hce zenon_H2bc zenon_H124 zenon_H298 zenon_H284 zenon_He0 zenon_H186 zenon_Hc6 zenon_H293 zenon_H29d zenon_H269 zenon_Hd5 zenon_He6 zenon_H24b zenon_H287 zenon_H2ae zenon_Hdf zenon_H17e zenon_H28f zenon_H272 zenon_H27c zenon_H18a zenon_H157 zenon_Hca zenon_H94 zenon_H5b zenon_H30e zenon_Hc0 zenon_H2f zenon_H12d zenon_H104 zenon_Hfd zenon_He9 zenon_H12a zenon_H85 zenon_H36 zenon_H99 zenon_H191 zenon_H100 zenon_H281 zenon_H289 zenon_H130 zenon_H303 zenon_H135 zenon_H14b zenon_H13d zenon_H2f5 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H1de zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_H244 zenon_H15e zenon_H1a3 zenon_H1a2 zenon_H47 zenon_H171 zenon_H182 zenon_Hdb zenon_Hf4. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.52 apply (zenon_L717_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.52 apply (zenon_L61_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.52 exact (zenon_H163 zenon_H103). % 10.36/10.52 apply (zenon_L735_); trivial. % 10.36/10.52 (* end of lemma zenon_L736_ *) % 10.36/10.52 assert (zenon_L737_ : ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H46 zenon_H2db zenon_Hce zenon_H2bc zenon_H124 zenon_H182 zenon_H298 zenon_H284 zenon_He0 zenon_H186 zenon_H293 zenon_H29d zenon_H269 zenon_Hd5 zenon_He6 zenon_H24b zenon_H287 zenon_H2ae zenon_Hdf zenon_H17e zenon_H28f zenon_H272 zenon_H27c zenon_H18a zenon_H157 zenon_Hca zenon_H94 zenon_H5b zenon_H30e zenon_Hc0 zenon_H2f zenon_H12d zenon_H104 zenon_Hfd zenon_He9 zenon_H12a zenon_H36 zenon_H99 zenon_H191 zenon_H100 zenon_H281 zenon_H289 zenon_H130 zenon_H303 zenon_H135 zenon_H14b zenon_H13d zenon_Hf4 zenon_H2f5 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H1de zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_H244 zenon_H15e zenon_H1a3 zenon_H1a2 zenon_H47 zenon_H171 zenon_H85 zenon_H74 zenon_Hdd zenon_Hc6. % 10.36/10.52 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.36/10.52 apply (zenon_L88_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.36/10.52 apply (zenon_L734_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.36/10.52 apply (zenon_L595_); trivial. % 10.36/10.52 apply (zenon_L238_); trivial. % 10.36/10.52 (* end of lemma zenon_L737_ *) % 10.36/10.52 assert (zenon_L738_ : (~((op (e0) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.36/10.52 do 0 intro. intros zenon_H45 zenon_H163 zenon_Hc4 zenon_H1ee zenon_H1eb zenon_H17c zenon_H1e5 zenon_Hc6 zenon_Hdd zenon_H85 zenon_H171 zenon_H47 zenon_H1a2 zenon_H1a3 zenon_H15e zenon_H244 zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H1de zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H2f5 zenon_Hf4 zenon_H13d zenon_H14b zenon_H135 zenon_H303 zenon_H130 zenon_H289 zenon_H281 zenon_H100 zenon_H191 zenon_H99 zenon_H36 zenon_H12a zenon_Hfd zenon_H104 zenon_H12d zenon_H2f zenon_Hc0 zenon_H30e zenon_H5b zenon_H94 zenon_Hca zenon_H157 zenon_H18a zenon_H27c zenon_H272 zenon_H28f zenon_H17e zenon_Hdf zenon_H2ae zenon_H287 zenon_H24b zenon_He6 zenon_Hd5 zenon_H269 zenon_H29d zenon_H293 zenon_H186 zenon_He0 zenon_H284 zenon_H298 zenon_H182 zenon_H124 zenon_H2bc zenon_Hce zenon_H2db zenon_H46 zenon_He9 zenon_H1ed. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.36/10.52 exact (zenon_H45 zenon_H42). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.36/10.52 apply (zenon_L594_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.36/10.52 apply (zenon_L35_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.36/10.52 exact (zenon_H163 zenon_H103). % 10.36/10.52 apply (zenon_L219_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.36/10.52 apply (zenon_L737_); trivial. % 10.36/10.52 apply (zenon_L185_); trivial. % 10.36/10.52 (* end of lemma zenon_L738_ *) % 10.36/10.52 assert (zenon_L739_ : ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.36/10.52 do 0 intro. intros zenon_H1ed zenon_H1e5 zenon_H16e zenon_Ha4 zenon_H163 zenon_H46 zenon_H2db zenon_Hce zenon_H2bc zenon_H124 zenon_H298 zenon_H284 zenon_He0 zenon_H186 zenon_Hc6 zenon_H293 zenon_H29d zenon_H269 zenon_Hd5 zenon_He6 zenon_H24b zenon_H287 zenon_H2ae zenon_Hdf zenon_H17e zenon_H28f zenon_H272 zenon_H27c zenon_H18a zenon_H157 zenon_Hca zenon_H94 zenon_H5b zenon_H30e zenon_Hc0 zenon_H2f zenon_H12d zenon_H104 zenon_Hfd zenon_He9 zenon_H12a zenon_H85 zenon_H36 zenon_H99 zenon_H191 zenon_H100 zenon_H281 zenon_H289 zenon_H130 zenon_H303 zenon_H135 zenon_H14b zenon_H13d zenon_H2f5 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H1de zenon_H2cf zenon_H2cd zenon_H26e zenon_H2ed zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_H244 zenon_H15e zenon_H1a3 zenon_H1a2 zenon_H47 zenon_H171 zenon_H182 zenon_Hdb zenon_Hf4. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.52 apply (zenon_L556_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.52 apply (zenon_L225_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.52 apply (zenon_L249_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.52 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.36/10.52 apply (zenon_L59_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.36/10.52 apply (zenon_L281_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.36/10.52 apply (zenon_L307_); trivial. % 10.36/10.52 apply (zenon_L551_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.52 apply (zenon_L107_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.52 exact (zenon_H163 zenon_H103). % 10.36/10.52 apply (zenon_L735_); trivial. % 10.36/10.52 (* end of lemma zenon_L739_ *) % 10.36/10.52 assert (zenon_L740_ : (~((op (e0) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.36/10.52 do 0 intro. intros zenon_H45 zenon_H1e5 zenon_H16e zenon_H1eb zenon_H1ee zenon_Hc4 zenon_Hc6 zenon_Hdd zenon_H85 zenon_H171 zenon_H47 zenon_H1a2 zenon_H1a3 zenon_H15e zenon_H244 zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H1de zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H2f5 zenon_Hf4 zenon_H13d zenon_H14b zenon_H135 zenon_H303 zenon_H130 zenon_H289 zenon_H281 zenon_H100 zenon_H191 zenon_H99 zenon_H36 zenon_H12a zenon_Hfd zenon_H104 zenon_H12d zenon_H2f zenon_Hc0 zenon_H30e zenon_H5b zenon_H94 zenon_Hca zenon_H157 zenon_H18a zenon_H27c zenon_H272 zenon_H28f zenon_H17e zenon_Hdf zenon_H2ae zenon_H287 zenon_H24b zenon_He6 zenon_Hd5 zenon_H269 zenon_H29d zenon_H293 zenon_H186 zenon_He0 zenon_H284 zenon_H298 zenon_H182 zenon_H124 zenon_H2bc zenon_Hce zenon_H2db zenon_H46 zenon_He9 zenon_H1ed. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.52 apply (zenon_L556_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.52 apply (zenon_L137_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.52 apply (zenon_L249_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.36/10.52 exact (zenon_H45 zenon_H42). % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.36/10.52 apply (zenon_L594_); trivial. % 10.36/10.52 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.36/10.52 apply (zenon_L737_); trivial. % 10.36/10.52 apply (zenon_L185_); trivial. % 10.36/10.52 (* end of lemma zenon_L740_ *) % 10.36/10.52 assert (zenon_L741_ : (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e3) (e3)) = (e1))) -> ((op (e0) (e2)) = (e1)) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.36/10.53 do 0 intro. intros zenon_H163 zenon_H45 zenon_H1e5 zenon_H16e zenon_H1eb zenon_H1ee zenon_Hc4 zenon_Hc6 zenon_H85 zenon_H171 zenon_H47 zenon_H1a2 zenon_H1a3 zenon_H15e zenon_H244 zenon_H2b9 zenon_H245 zenon_H262 zenon_H154 zenon_H202 zenon_H2ef zenon_H2f2 zenon_H2ed zenon_H26e zenon_H2cd zenon_H2cf zenon_H1de zenon_H2ea zenon_H1b2 zenon_H173 zenon_H115 zenon_H9c zenon_H177 zenon_H2e7 zenon_H2e4 zenon_H2f5 zenon_Hf4 zenon_H13d zenon_H14b zenon_H135 zenon_H303 zenon_H130 zenon_H289 zenon_H281 zenon_H100 zenon_H191 zenon_H99 zenon_H36 zenon_H12a zenon_Hfd zenon_H104 zenon_H12d zenon_H2f zenon_Hc0 zenon_H30e zenon_H5b zenon_H94 zenon_Hca zenon_H157 zenon_H18a zenon_H27c zenon_H272 zenon_H28f zenon_H17e zenon_Hdf zenon_H2ae zenon_H287 zenon_H24b zenon_He6 zenon_Hd5 zenon_H269 zenon_H29d zenon_H293 zenon_H186 zenon_He0 zenon_H284 zenon_H298 zenon_H182 zenon_H124 zenon_H2bc zenon_Hce zenon_H2db zenon_H46 zenon_He9 zenon_H1ed. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.53 apply (zenon_L511_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.53 apply (zenon_L310_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.53 apply (zenon_L739_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.53 apply (zenon_L310_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.53 apply (zenon_L45_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.53 apply (zenon_L556_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.53 apply (zenon_L225_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.53 apply (zenon_L249_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.53 apply (zenon_L707_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.53 apply (zenon_L107_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.53 exact (zenon_H163 zenon_H103). % 10.36/10.53 apply (zenon_L735_); trivial. % 10.36/10.53 apply (zenon_L740_); trivial. % 10.36/10.53 (* end of lemma zenon_L741_ *) % 10.36/10.53 assert (zenon_L742_ : ((op (e0) (e0)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H5a zenon_H1ed zenon_He9 zenon_H46 zenon_H2db zenon_Hce zenon_H2bc zenon_H124 zenon_H182 zenon_H298 zenon_H284 zenon_He0 zenon_H186 zenon_H293 zenon_H29d zenon_H269 zenon_Hd5 zenon_He6 zenon_H24b zenon_H287 zenon_H2ae zenon_Hdf zenon_H17e zenon_H28f zenon_H272 zenon_H27c zenon_H18a zenon_H157 zenon_Hca zenon_H94 zenon_H5b zenon_H30e zenon_Hc0 zenon_H2f zenon_H12d zenon_H104 zenon_Hfd zenon_H12a zenon_H36 zenon_H99 zenon_H191 zenon_H100 zenon_H281 zenon_H289 zenon_H130 zenon_H303 zenon_H135 zenon_H14b zenon_H13d zenon_Hf4 zenon_H2f5 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H1de zenon_H26e zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_H244 zenon_H15e zenon_H1a3 zenon_H1a2 zenon_H47 zenon_H171 zenon_H85 zenon_Hc6 zenon_H16e zenon_H45 zenon_H163 zenon_H2cf zenon_H2ed zenon_H1e5 zenon_H1ee zenon_H1eb zenon_H2cd. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.53 apply (zenon_L597_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.53 apply (zenon_L312_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.53 apply (zenon_L741_); trivial. % 10.36/10.53 apply (zenon_L526_); trivial. % 10.36/10.53 (* end of lemma zenon_L742_ *) % 10.36/10.53 assert (zenon_L743_ : ((op (e0) (e1)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e1) = (e2))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H119 zenon_H1ed zenon_He9 zenon_H46 zenon_H2db zenon_Hce zenon_H2bc zenon_H124 zenon_H182 zenon_H298 zenon_H284 zenon_He0 zenon_H186 zenon_H293 zenon_H29d zenon_H269 zenon_Hd5 zenon_He6 zenon_H24b zenon_H287 zenon_H2ae zenon_Hdf zenon_H17e zenon_H28f zenon_H272 zenon_H27c zenon_H18a zenon_H157 zenon_Hca zenon_H94 zenon_H5b zenon_H30e zenon_Hc0 zenon_H2f zenon_H12d zenon_H104 zenon_Hfd zenon_H12a zenon_H36 zenon_H99 zenon_H191 zenon_H100 zenon_H281 zenon_H289 zenon_H130 zenon_H303 zenon_H135 zenon_H14b zenon_H13d zenon_Hf4 zenon_H2f5 zenon_H2e4 zenon_H2e7 zenon_H177 zenon_H9c zenon_H115 zenon_H173 zenon_H1b2 zenon_H2ea zenon_H1de zenon_H26e zenon_H2f2 zenon_H2ef zenon_H202 zenon_H154 zenon_H262 zenon_H245 zenon_H2b9 zenon_H244 zenon_H15e zenon_H1a3 zenon_H1a2 zenon_H47 zenon_H171 zenon_H85 zenon_Hc6 zenon_H16e zenon_H45 zenon_H163 zenon_H2cf zenon_H2ed zenon_H1e5 zenon_H1ee zenon_H1eb zenon_H2cd. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.53 apply (zenon_L134_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.53 apply (zenon_L312_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.53 apply (zenon_L741_); trivial. % 10.36/10.53 apply (zenon_L526_); trivial. % 10.36/10.53 (* end of lemma zenon_L743_ *) % 10.36/10.53 assert (zenon_L744_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H3c zenon_H51 zenon_Hf4. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H2d. zenon_intro zenon_H3d. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H2f. zenon_intro zenon_H80. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.36/10.53 apply (zenon_L328_); trivial. % 10.36/10.53 (* end of lemma zenon_L744_ *) % 10.36/10.53 assert (zenon_L745_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H303 zenon_H37 zenon_H2d zenon_H2f zenon_H44 zenon_H13b zenon_H130. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H1f | zenon_intro zenon_H304 ]. % 10.36/10.53 apply (zenon_L7_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H31 | zenon_intro zenon_H305 ]. % 10.36/10.53 exact (zenon_H2f zenon_H31). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H46 | zenon_intro zenon_H5a ]. % 10.36/10.53 exact (zenon_H44 zenon_H46). % 10.36/10.53 apply (zenon_L133_); trivial. % 10.36/10.53 (* end of lemma zenon_L745_ *) % 10.36/10.53 assert (zenon_L746_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 10.36/10.53 do 0 intro. intros zenon_Hdf zenon_Hf4 zenon_H6a zenon_H8c zenon_H182 zenon_H51 zenon_H24b zenon_He5. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.53 apply (zenon_L236_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.53 exact (zenon_H8c zenon_H91). % 10.36/10.53 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.53 apply (zenon_L307_); trivial. % 10.36/10.53 apply (zenon_L213_); trivial. % 10.36/10.53 (* end of lemma zenon_L746_ *) % 10.36/10.53 assert (zenon_L747_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H1a3 zenon_H44 zenon_H85 zenon_H2d zenon_Hce zenon_Hdf zenon_Hf4 zenon_H6a zenon_H8c zenon_H182 zenon_H51 zenon_H24b. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.53 exact (zenon_H44 zenon_H46). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.53 apply (zenon_L486_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.53 apply (zenon_L48_); trivial. % 10.36/10.53 apply (zenon_L746_); trivial. % 10.36/10.53 (* end of lemma zenon_L747_ *) % 10.36/10.53 assert (zenon_L748_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H1a3 zenon_H44 zenon_H85 zenon_Hce zenon_H51 zenon_H15e zenon_Hfa zenon_He9 zenon_H2d zenon_H27c zenon_H1ed zenon_Hfd. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.53 exact (zenon_H44 zenon_H46). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.53 apply (zenon_L486_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.53 apply (zenon_L48_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.53 apply (zenon_L383_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.53 apply (zenon_L134_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.53 apply (zenon_L252_); trivial. % 10.36/10.53 apply (zenon_L103_); trivial. % 10.36/10.53 (* end of lemma zenon_L748_ *) % 10.36/10.53 assert (zenon_L749_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H191 zenon_H2f zenon_H24b zenon_H182 zenon_H8c zenon_Hf4 zenon_Hdf zenon_Hfd zenon_H1ed zenon_H27c zenon_H2d zenon_He9 zenon_H15e zenon_H51 zenon_Hce zenon_H85 zenon_H44 zenon_H1a3 zenon_H189 zenon_H26e. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.53 exact (zenon_H2f zenon_H31). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.53 apply (zenon_L747_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.53 apply (zenon_L748_); trivial. % 10.36/10.53 apply (zenon_L380_); trivial. % 10.36/10.53 (* end of lemma zenon_L749_ *) % 10.36/10.53 assert (zenon_L750_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e1)) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H4b zenon_H8c. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H42. zenon_intro zenon_H4c. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H44. zenon_intro zenon_H8f. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.36/10.53 exact (zenon_H8c zenon_H91). % 10.36/10.53 (* end of lemma zenon_L750_ *) % 10.36/10.53 assert (zenon_L751_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H52 zenon_H1ee. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H42. zenon_intro zenon_H53. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H44. zenon_intro zenon_H1c8. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.36/10.53 exact (zenon_H1ee zenon_Hd3). % 10.36/10.53 (* end of lemma zenon_L751_ *) % 10.36/10.53 assert (zenon_L752_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H303 zenon_H5b zenon_H56 zenon_Ha4 zenon_H287 zenon_H51 zenon_Hc0 zenon_H1b2 zenon_Hc4 zenon_H28c zenon_H44 zenon_H58. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H1f | zenon_intro zenon_H304 ]. % 10.36/10.53 apply (zenon_L16_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H31 | zenon_intro zenon_H305 ]. % 10.36/10.53 apply (zenon_L302_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H46 | zenon_intro zenon_H5a ]. % 10.36/10.53 exact (zenon_H44 zenon_H46). % 10.36/10.53 exact (zenon_H58 zenon_H5a). % 10.36/10.53 (* end of lemma zenon_L752_ *) % 10.36/10.53 assert (zenon_L753_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e2)) -> False). % 10.36/10.53 do 0 intro. intros zenon_H14b zenon_Ha4 zenon_H252. % 10.36/10.53 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H14b. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_Ha4. % 10.36/10.53 cut (((e2) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2bf]. % 10.36/10.53 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 10.36/10.53 congruence. % 10.36/10.53 apply zenon_H39. apply refl_equal. % 10.36/10.53 apply zenon_H2bf. apply sym_equal. exact zenon_H252. % 10.36/10.53 (* end of lemma zenon_L753_ *) % 10.36/10.53 assert (zenon_L754_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 10.36/10.53 do 0 intro. intros zenon_H278 zenon_H51 zenon_H2d9. % 10.36/10.53 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H278. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_H51. % 10.36/10.53 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H2da]. % 10.36/10.53 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 10.36/10.53 congruence. % 10.36/10.53 apply zenon_Hd0. apply refl_equal. % 10.36/10.53 apply zenon_H2da. apply sym_equal. exact zenon_H2d9. % 10.36/10.53 (* end of lemma zenon_L754_ *) % 10.36/10.53 assert (zenon_L755_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H2db zenon_H13b zenon_Hfd zenon_Ha4 zenon_H14b zenon_H51 zenon_H278 zenon_H1ee. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H136 | zenon_intro zenon_H2dc ]. % 10.36/10.53 apply (zenon_L255_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H252 | zenon_intro zenon_H2dd ]. % 10.36/10.53 apply (zenon_L753_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H2d9 | zenon_intro zenon_Hd3 ]. % 10.36/10.53 apply (zenon_L754_); trivial. % 10.36/10.53 exact (zenon_H1ee zenon_Hd3). % 10.36/10.53 (* end of lemma zenon_L755_ *) % 10.36/10.53 assert (zenon_L756_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H1a3 zenon_H44 zenon_H1ee zenon_H278 zenon_H14b zenon_Hfd zenon_H13b zenon_H2db zenon_Hce zenon_H51 zenon_H56 zenon_H85. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.53 exact (zenon_H44 zenon_H46). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.53 apply (zenon_L755_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.53 apply (zenon_L48_); trivial. % 10.36/10.53 apply (zenon_L663_); trivial. % 10.36/10.53 (* end of lemma zenon_L756_ *) % 10.36/10.53 assert (zenon_L757_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H70 zenon_H51 zenon_H85. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H6a. zenon_intro zenon_H72. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H6b. zenon_intro zenon_H27. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.36/10.53 apply (zenon_L595_); trivial. % 10.36/10.53 (* end of lemma zenon_L757_ *) % 10.36/10.53 assert (zenon_L758_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H12d zenon_H85 zenon_Ha4 zenon_H8c zenon_H177 zenon_H6a zenon_H6b zenon_Hb3 zenon_H51 zenon_H182 zenon_Hf4 zenon_Hdf zenon_H79 zenon_H2ed. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.53 apply (zenon_L486_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.53 exact (zenon_H6b zenon_H6f). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.53 apply (zenon_L236_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.53 exact (zenon_H8c zenon_H91). % 10.36/10.53 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.53 apply (zenon_L307_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.36/10.53 exact (zenon_H6b zenon_H6f). % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.36/10.53 apply (zenon_L282_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.36/10.53 exact (zenon_H8c zenon_H91). % 10.36/10.53 apply (zenon_L137_); trivial. % 10.36/10.53 apply (zenon_L525_); trivial. % 10.36/10.53 (* end of lemma zenon_L758_ *) % 10.36/10.53 assert (zenon_L759_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e0) (e0)) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H89 zenon_H44. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8c. zenon_intro zenon_H43. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.36/10.53 exact (zenon_H44 zenon_H46). % 10.36/10.53 (* end of lemma zenon_L759_ *) % 10.36/10.53 assert (zenon_L760_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H18f zenon_H1ee. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H8b. zenon_intro zenon_H190. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H190). zenon_intro zenon_H8c. zenon_intro zenon_H1c8. % 10.36/10.53 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.36/10.53 exact (zenon_H1ee zenon_Hd3). % 10.36/10.53 (* end of lemma zenon_L760_ *) % 10.36/10.53 assert (zenon_L761_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e0)) = (e1)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H2c5 zenon_H5a zenon_Hfa zenon_Hf4 zenon_Hef zenon_H51 zenon_H28f zenon_H1ee. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.36/10.53 apply (zenon_L383_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.36/10.53 apply (zenon_L97_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.36/10.53 apply (zenon_L264_); trivial. % 10.36/10.53 exact (zenon_H1ee zenon_Hd3). % 10.36/10.53 (* end of lemma zenon_L761_ *) % 10.36/10.53 assert (zenon_L762_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e2) (e1)) = (e0)) -> False). % 10.36/10.53 do 0 intro. intros zenon_H171 zenon_H6f zenon_Hc4. % 10.36/10.53 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H171. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_H6f. % 10.36/10.53 cut (((e0) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H286]. % 10.36/10.53 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 10.36/10.53 congruence. % 10.36/10.53 apply zenon_H172. apply refl_equal. % 10.36/10.53 apply zenon_H286. apply sym_equal. exact zenon_Hc4. % 10.36/10.53 (* end of lemma zenon_L762_ *) % 10.36/10.53 assert (zenon_L763_ : (~((op (e1) (op (e1) (e1))) = (op (e1) (e0)))) -> ((op (e1) (e1)) = (e0)) -> False). % 10.36/10.53 do 0 intro. intros zenon_H311 zenon_H6f. % 10.36/10.53 cut (((op (e1) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 10.36/10.53 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.36/10.53 congruence. % 10.36/10.53 apply zenon_H98. apply refl_equal. % 10.36/10.53 exact (zenon_H6b zenon_H6f). % 10.36/10.53 (* end of lemma zenon_L763_ *) % 10.36/10.53 assert (zenon_L764_ : ((op (e2) (e1)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((e3) = (op (op (e1) (op (e1) (e1))) (e1)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H120 zenon_Hba zenon_H6f zenon_H11a. % 10.36/10.53 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.36/10.53 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((e3) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H11a. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_Ha7. % 10.36/10.53 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.36/10.53 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 10.36/10.53 congruence. % 10.36/10.53 cut (((op (e2) (e1)) = (e3)) = ((op (op (e1) (op (e1) (e1))) (e1)) = (e3))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H11b. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_H120. % 10.36/10.53 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.36/10.53 cut (((op (e2) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 10.36/10.53 congruence. % 10.36/10.53 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.36/10.53 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((op (e2) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H19e. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_Ha7. % 10.36/10.53 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.36/10.53 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 10.36/10.53 congruence. % 10.36/10.53 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.36/10.53 cut (((op (e1) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 10.36/10.53 congruence. % 10.36/10.53 cut (((op (e1) (e0)) = (e2)) = ((op (e1) (op (e1) (e1))) = (e2))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H19c. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_Hba. % 10.36/10.53 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.36/10.53 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H312]. % 10.36/10.53 congruence. % 10.36/10.53 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.36/10.53 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e1) (e1))))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H312. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_Hae. % 10.36/10.53 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.36/10.53 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H311]. % 10.36/10.53 congruence. % 10.36/10.53 apply (zenon_L763_); trivial. % 10.36/10.53 apply zenon_Haf. apply refl_equal. % 10.36/10.53 apply zenon_Haf. apply refl_equal. % 10.36/10.53 apply zenon_H87. apply refl_equal. % 10.36/10.53 apply zenon_H98. apply refl_equal. % 10.36/10.53 apply zenon_Ha8. apply refl_equal. % 10.36/10.53 apply zenon_Ha8. apply refl_equal. % 10.36/10.53 apply zenon_Heb. apply refl_equal. % 10.36/10.53 apply zenon_Ha8. apply refl_equal. % 10.36/10.53 apply zenon_Ha8. apply refl_equal. % 10.36/10.53 (* end of lemma zenon_L764_ *) % 10.36/10.53 assert (zenon_L765_ : ((op (e2) (e1)) = (e3)) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 10.36/10.53 do 0 intro. intros zenon_H120 zenon_Hba zenon_H6f. % 10.36/10.53 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H314 | zenon_intro zenon_H313 ]. % 10.36/10.53 apply zenon_H314. apply sym_equal. exact zenon_H6f. % 10.36/10.53 apply (zenon_notand_s _ _ zenon_H313); [ zenon_intro zenon_H19b | zenon_intro zenon_H11a ]. % 10.36/10.53 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.36/10.53 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((e2) = (op (e1) (op (e1) (e1))))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H19b. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_Hae. % 10.36/10.53 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.36/10.53 cut (((op (e1) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 10.36/10.53 congruence. % 10.36/10.53 cut (((op (e1) (e0)) = (e2)) = ((op (e1) (op (e1) (e1))) = (e2))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H19c. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_Hba. % 10.36/10.53 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.36/10.53 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H312]. % 10.36/10.53 congruence. % 10.36/10.53 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.36/10.53 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e1) (e1))))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H312. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_Hae. % 10.36/10.53 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.36/10.53 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H311]. % 10.36/10.53 congruence. % 10.36/10.53 apply (zenon_L763_); trivial. % 10.36/10.53 apply zenon_Haf. apply refl_equal. % 10.36/10.53 apply zenon_Haf. apply refl_equal. % 10.36/10.53 apply zenon_H87. apply refl_equal. % 10.36/10.53 apply zenon_Haf. apply refl_equal. % 10.36/10.53 apply zenon_Haf. apply refl_equal. % 10.36/10.53 apply (zenon_L764_); trivial. % 10.36/10.53 (* end of lemma zenon_L765_ *) % 10.36/10.53 assert (zenon_L766_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.36/10.53 do 0 intro. intros zenon_Hb3 zenon_Hba zenon_H120 zenon_H115 zenon_Hef zenon_H8c zenon_Ha3. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.36/10.53 apply (zenon_L765_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.36/10.53 apply (zenon_L65_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.36/10.53 exact (zenon_H8c zenon_H91). % 10.36/10.53 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.53 (* end of lemma zenon_L766_ *) % 10.36/10.53 assert (zenon_L767_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 10.36/10.53 do 0 intro. intros zenon_H262 zenon_H6f zenon_H128. % 10.36/10.53 cut (((op (e1) (e1)) = (e0)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_H262. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_H6f. % 10.36/10.53 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H26d]. % 10.36/10.53 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 10.36/10.53 congruence. % 10.36/10.53 apply zenon_H172. apply refl_equal. % 10.36/10.53 apply zenon_H26d. apply sym_equal. exact zenon_H128. % 10.36/10.53 (* end of lemma zenon_L767_ *) % 10.36/10.53 assert (zenon_L768_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.36/10.53 do 0 intro. intros zenon_Hb3 zenon_H128 zenon_H262 zenon_H115 zenon_Hef zenon_H8c zenon_Ha3. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.36/10.53 apply (zenon_L767_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.36/10.53 apply (zenon_L65_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.36/10.53 exact (zenon_H8c zenon_H91). % 10.36/10.53 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.53 (* end of lemma zenon_L768_ *) % 10.36/10.53 assert (zenon_L769_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H244 zenon_H1ee zenon_H278 zenon_H51 zenon_Ha4 zenon_Hfd zenon_H2db zenon_H14b zenon_H119 zenon_H241 zenon_He9 zenon_H159 zenon_Hd5. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.36/10.53 apply (zenon_L755_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.36/10.53 apply (zenon_L90_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.36/10.53 apply (zenon_L185_); trivial. % 10.36/10.53 apply (zenon_L397_); trivial. % 10.36/10.53 (* end of lemma zenon_L769_ *) % 10.36/10.53 assert (zenon_L770_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_Hca zenon_H6f zenon_H171 zenon_H85 zenon_H15b zenon_H5a zenon_Hc0 zenon_Hba zenon_H245 zenon_H1f zenon_H130 zenon_Ha3 zenon_H8c zenon_Hef zenon_H115 zenon_H262 zenon_Hb3 zenon_He9 zenon_H119 zenon_H14b zenon_H2db zenon_Hfd zenon_Ha4 zenon_H51 zenon_H278 zenon_H1ee zenon_H244 zenon_Hd5. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.36/10.53 apply (zenon_L44_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.36/10.53 apply (zenon_L762_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.36/10.53 apply (zenon_L595_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.36/10.53 apply (zenon_L384_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.36/10.53 apply (zenon_L766_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.36/10.53 apply (zenon_L60_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.53 apply (zenon_L81_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.53 apply (zenon_L768_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.53 apply (zenon_L769_); trivial. % 10.36/10.53 apply (zenon_L506_); trivial. % 10.36/10.53 (* end of lemma zenon_L770_ *) % 10.36/10.53 assert (zenon_L771_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.36/10.53 do 0 intro. intros zenon_Hb3 zenon_Hc4 zenon_H171 zenon_H115 zenon_Hef zenon_H8c zenon_Ha3. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.36/10.53 apply (zenon_L762_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.36/10.53 apply (zenon_L65_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.36/10.53 exact (zenon_H8c zenon_H91). % 10.36/10.53 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.53 (* end of lemma zenon_L771_ *) % 10.36/10.53 assert (zenon_L772_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H2db zenon_H85 zenon_H131 zenon_H127 zenon_Hfd zenon_H51 zenon_H278 zenon_H1ee. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H136 | zenon_intro zenon_H2dc ]. % 10.36/10.53 apply (zenon_L628_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H252 | zenon_intro zenon_H2dd ]. % 10.36/10.53 apply (zenon_L199_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H2d9 | zenon_intro zenon_Hd3 ]. % 10.36/10.53 apply (zenon_L754_); trivial. % 10.36/10.53 exact (zenon_H1ee zenon_Hd3). % 10.36/10.53 (* end of lemma zenon_L772_ *) % 10.36/10.53 assert (zenon_L773_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H244 zenon_H130 zenon_H5a zenon_H252 zenon_Hfd zenon_H241 zenon_He9 zenon_H159 zenon_Hd5. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.36/10.53 apply (zenon_L133_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.36/10.53 apply (zenon_L199_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.36/10.53 apply (zenon_L185_); trivial. % 10.36/10.53 apply (zenon_L397_); trivial. % 10.36/10.53 (* end of lemma zenon_L773_ *) % 10.36/10.53 assert (zenon_L774_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e3)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H2db zenon_Hc0 zenon_H135 zenon_He5 zenon_H1f zenon_H28c zenon_Hd5 zenon_H159 zenon_He9 zenon_H241 zenon_Hfd zenon_H5a zenon_H130 zenon_H244 zenon_H51 zenon_H278 zenon_H1ee. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H136 | zenon_intro zenon_H2dc ]. % 10.36/10.53 apply (zenon_L385_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H252 | zenon_intro zenon_H2dd ]. % 10.36/10.53 apply (zenon_L773_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H2d9 | zenon_intro zenon_Hd3 ]. % 10.36/10.53 apply (zenon_L754_); trivial. % 10.36/10.53 exact (zenon_H1ee zenon_Hd3). % 10.36/10.53 (* end of lemma zenon_L774_ *) % 10.36/10.53 assert (zenon_L775_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e2) = (e3))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H2b9 zenon_H85 zenon_H51 zenon_H2a5 zenon_H12a zenon_He9 zenon_H2d zenon_Ha3 zenon_H8c zenon_Hef zenon_H115 zenon_Hba zenon_Hb3 zenon_Hfd. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.53 apply (zenon_L486_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.53 exact (zenon_H8c zenon_H91). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.53 apply (zenon_L287_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.53 apply (zenon_L134_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.53 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.53 apply (zenon_L766_); trivial. % 10.36/10.53 apply (zenon_L199_); trivial. % 10.36/10.53 (* end of lemma zenon_L775_ *) % 10.36/10.53 assert (zenon_L776_ : ((op (e1) (e1)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H6f zenon_Ha2 zenon_He9. % 10.36/10.53 elim (classic ((e3) = (e3))); [ zenon_intro zenon_Hea | zenon_intro zenon_Heb ]. % 10.36/10.53 cut (((e3) = (e3)) = ((e0) = (e3))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_He9. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_Hea. % 10.36/10.53 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.36/10.53 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hec]. % 10.36/10.53 congruence. % 10.36/10.53 cut (((op (e1) (e1)) = (e0)) = ((e3) = (e0))). % 10.36/10.53 intro zenon_D_pnotp. % 10.36/10.53 apply zenon_Hec. % 10.36/10.53 rewrite <- zenon_D_pnotp. % 10.36/10.53 exact zenon_H6f. % 10.36/10.53 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 10.36/10.53 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 10.36/10.53 congruence. % 10.36/10.53 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.53 apply zenon_H84. apply refl_equal. % 10.36/10.53 apply zenon_Heb. apply refl_equal. % 10.36/10.53 apply zenon_Heb. apply refl_equal. % 10.36/10.53 (* end of lemma zenon_L776_ *) % 10.36/10.53 assert (zenon_L777_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.36/10.53 do 0 intro. intros zenon_H2b9 zenon_Hf4 zenon_H177 zenon_H51 zenon_H2a5 zenon_H12a zenon_H104 zenon_Hf6 zenon_He9 zenon_H6f zenon_Hba zenon_Hfd. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.53 apply (zenon_L89_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.53 apply (zenon_L197_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.53 apply (zenon_L287_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.53 apply (zenon_L99_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.53 apply (zenon_L776_); trivial. % 10.36/10.53 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.53 apply (zenon_L765_); trivial. % 10.36/10.53 apply (zenon_L199_); trivial. % 10.36/10.53 (* end of lemma zenon_L777_ *) % 10.36/10.53 assert (zenon_L778_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e1)) = (e2)) -> (~((e2) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e1)) -> False). % 10.36/10.53 do 0 intro. intros zenon_H12a zenon_Hd5 zenon_H244 zenon_H1ee zenon_H278 zenon_H51 zenon_Ha4 zenon_Hfd zenon_H2db zenon_H14b zenon_He9 zenon_H99 zenon_H130 zenon_H1f zenon_H245 zenon_H100 zenon_Hc0 zenon_H5a zenon_H15b zenon_H85 zenon_H171 zenon_Hca zenon_Ha3 zenon_H6f zenon_Hba zenon_H104 zenon_H175. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.36/10.54 apply (zenon_L44_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.36/10.54 apply (zenon_L762_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.36/10.54 apply (zenon_L595_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.36/10.54 apply (zenon_L384_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.36/10.54 apply (zenon_L212_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.36/10.54 apply (zenon_L60_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.54 apply (zenon_L81_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.54 apply (zenon_L111_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.54 apply (zenon_L769_); trivial. % 10.36/10.54 apply (zenon_L506_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.54 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.54 apply (zenon_L765_); trivial. % 10.36/10.54 apply (zenon_L187_); trivial. % 10.36/10.54 (* end of lemma zenon_L778_ *) % 10.36/10.54 assert (zenon_L779_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e0) (e0)) = (e3)) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H191 zenon_H104 zenon_H138 zenon_H1ee zenon_H28f zenon_H51 zenon_Hef zenon_Hf4 zenon_H5a zenon_H2c5 zenon_H131 zenon_H99. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.54 apply (zenon_L295_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.54 apply (zenon_L84_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.54 apply (zenon_L761_); trivial. % 10.36/10.54 apply (zenon_L110_); trivial. % 10.36/10.54 (* end of lemma zenon_L779_ *) % 10.36/10.54 assert (zenon_L780_ : (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e3)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H2e0 zenon_H173 zenon_H6f zenon_H175 zenon_H252 zenon_H14b zenon_H100 zenon_H120. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e1 ]. % 10.36/10.54 apply (zenon_L504_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H2e2 ]. % 10.36/10.54 apply (zenon_L124_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H119 ]. % 10.36/10.54 apply (zenon_L753_); trivial. % 10.36/10.54 apply (zenon_L212_); trivial. % 10.36/10.54 (* end of lemma zenon_L780_ *) % 10.36/10.54 assert (zenon_L781_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hb3 zenon_H120 zenon_H100 zenon_H14b zenon_H252 zenon_H175 zenon_H173 zenon_H2e0 zenon_H115 zenon_Hef zenon_H8c zenon_Ha3. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.36/10.54 apply (zenon_L780_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.36/10.54 apply (zenon_L65_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.36/10.54 exact (zenon_H8c zenon_H91). % 10.36/10.54 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.54 (* end of lemma zenon_L781_ *) % 10.36/10.54 assert (zenon_L782_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e1) (e0)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e2) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e0)) = (e1)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H2b9 zenon_Hba zenon_H6f zenon_Hca zenon_H171 zenon_H85 zenon_H1f zenon_H2db zenon_H278 zenon_H2a5 zenon_H17e zenon_H94 zenon_Hfd zenon_Hb3 zenon_H100 zenon_H14b zenon_H175 zenon_H173 zenon_H2e0 zenon_H115 zenon_H8c zenon_Ha3 zenon_H15b zenon_Hc0 zenon_H245 zenon_H2c5 zenon_Hf4 zenon_H51 zenon_H28f zenon_H1ee zenon_H138 zenon_H191 zenon_H99 zenon_Hd5 zenon_H133 zenon_H244 zenon_H130 zenon_H5a zenon_H186 zenon_He9 zenon_H12a zenon_Hef zenon_H104. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.54 apply (zenon_L778_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.54 exact (zenon_H8c zenon_H91). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.54 apply (zenon_L287_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.54 apply (zenon_L359_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.54 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.36/10.54 apply (zenon_L384_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.36/10.54 apply (zenon_L212_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.36/10.54 apply (zenon_L60_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.54 apply (zenon_L779_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.54 apply (zenon_L111_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.36/10.54 apply (zenon_L123_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.36/10.54 apply (zenon_L187_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.36/10.54 apply (zenon_L185_); trivial. % 10.36/10.54 apply (zenon_L397_); trivial. % 10.36/10.54 apply (zenon_L549_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.54 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.54 apply (zenon_L781_); trivial. % 10.36/10.54 apply (zenon_L199_); trivial. % 10.36/10.54 apply (zenon_L341_); trivial. % 10.36/10.54 (* end of lemma zenon_L782_ *) % 10.36/10.54 assert (zenon_L783_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hed zenon_H1a2 zenon_H104 zenon_Hc6 zenon_H51 zenon_Hf4 zenon_H100 zenon_H2c5 zenon_H28f zenon_H1ee zenon_H124 zenon_H99 zenon_H42 zenon_H24b. % 10.36/10.54 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hef. zenon_intro zenon_Hee. % 10.36/10.54 apply (zenon_and_s _ _ zenon_Hee). zenon_intro zenon_Ha3. zenon_intro zenon_H57. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.54 apply (zenon_L295_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.54 apply (zenon_L761_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.54 apply (zenon_L61_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.54 apply (zenon_L328_); trivial. % 10.36/10.54 apply (zenon_L75_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.54 apply (zenon_L421_); trivial. % 10.36/10.54 apply (zenon_L191_); trivial. % 10.36/10.54 (* end of lemma zenon_L783_ *) % 10.36/10.54 assert (zenon_L784_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H16f zenon_H51 zenon_Hfd. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hef. zenon_intro zenon_H170. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_Ha3. zenon_intro zenon_H1d3. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.36/10.54 apply (zenon_L60_); trivial. % 10.36/10.54 (* end of lemma zenon_L784_ *) % 10.36/10.54 assert (zenon_L785_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1ac zenon_H287 zenon_H51. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_Hb9. zenon_intro zenon_H1ad. % 10.36/10.54 apply (zenon_L299_); trivial. % 10.36/10.54 (* end of lemma zenon_L785_ *) % 10.36/10.54 assert (zenon_L786_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1b7 zenon_H2a5 zenon_H51. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.36/10.54 apply (zenon_L287_); trivial. % 10.36/10.54 (* end of lemma zenon_L786_ *) % 10.36/10.54 assert (zenon_L787_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H28c zenon_H1f zenon_H31 zenon_Hc0 zenon_H51 zenon_H287 zenon_H13b zenon_H135. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H28d ]. % 10.36/10.54 apply (zenon_L44_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_Hfa | zenon_intro zenon_H28e ]. % 10.36/10.54 apply (zenon_L121_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H152 ]. % 10.36/10.54 apply (zenon_L299_); trivial. % 10.36/10.54 apply (zenon_L211_); trivial. % 10.36/10.54 (* end of lemma zenon_L787_ *) % 10.36/10.54 assert (zenon_L788_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H281 zenon_H44 zenon_H6f zenon_He9 zenon_Hf6 zenon_H104 zenon_H12a zenon_H2a5 zenon_H177 zenon_Hf4 zenon_H2b9 zenon_H51 zenon_H287 zenon_Hfd zenon_H13b. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.54 exact (zenon_H44 zenon_H46). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.54 apply (zenon_L777_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.54 apply (zenon_L299_); trivial. % 10.36/10.54 apply (zenon_L255_); trivial. % 10.36/10.54 (* end of lemma zenon_L788_ *) % 10.36/10.54 assert (zenon_L789_ : ((op (e3) (e1)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> (~((e2) = (op (op (e1) (op (e1) (e1))) (e1)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H252 zenon_H13c zenon_H6f zenon_Ha6. % 10.36/10.54 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.36/10.54 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((e2) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.36/10.54 intro zenon_D_pnotp. % 10.36/10.54 apply zenon_Ha6. % 10.36/10.54 rewrite <- zenon_D_pnotp. % 10.36/10.54 exact zenon_Ha7. % 10.36/10.54 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.36/10.54 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 10.36/10.54 congruence. % 10.36/10.54 cut (((op (e3) (e1)) = (e2)) = ((op (op (e1) (op (e1) (e1))) (e1)) = (e2))). % 10.36/10.54 intro zenon_D_pnotp. % 10.36/10.54 apply zenon_Ha9. % 10.36/10.54 rewrite <- zenon_D_pnotp. % 10.36/10.54 exact zenon_H252. % 10.36/10.54 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 10.36/10.54 cut (((op (e3) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 10.36/10.54 congruence. % 10.36/10.54 elim (classic ((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 10.36/10.54 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1))) = ((op (e3) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))). % 10.36/10.54 intro zenon_D_pnotp. % 10.36/10.54 apply zenon_H2c3. % 10.36/10.54 rewrite <- zenon_D_pnotp. % 10.36/10.54 exact zenon_Ha7. % 10.36/10.54 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (op (e1) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 10.36/10.54 cut (((op (op (e1) (op (e1) (e1))) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2c4]. % 10.36/10.54 congruence. % 10.36/10.54 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 10.36/10.54 cut (((op (e1) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 10.36/10.54 congruence. % 10.36/10.54 cut (((op (e1) (e0)) = (e3)) = ((op (e1) (op (e1) (e1))) = (e3))). % 10.36/10.54 intro zenon_D_pnotp. % 10.36/10.54 apply zenon_H2c2. % 10.36/10.54 rewrite <- zenon_D_pnotp. % 10.36/10.54 exact zenon_H13c. % 10.36/10.54 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.36/10.54 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H312]. % 10.36/10.54 congruence. % 10.36/10.54 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.36/10.54 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e1) (e1))))). % 10.36/10.54 intro zenon_D_pnotp. % 10.36/10.54 apply zenon_H312. % 10.36/10.54 rewrite <- zenon_D_pnotp. % 10.36/10.54 exact zenon_Hae. % 10.36/10.54 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.36/10.54 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H311]. % 10.36/10.54 congruence. % 10.36/10.54 apply (zenon_L763_); trivial. % 10.36/10.54 apply zenon_Haf. apply refl_equal. % 10.36/10.54 apply zenon_Haf. apply refl_equal. % 10.36/10.54 apply zenon_Heb. apply refl_equal. % 10.36/10.54 apply zenon_H98. apply refl_equal. % 10.36/10.54 apply zenon_Ha8. apply refl_equal. % 10.36/10.54 apply zenon_Ha8. apply refl_equal. % 10.36/10.54 apply zenon_H87. apply refl_equal. % 10.36/10.54 apply zenon_Ha8. apply refl_equal. % 10.36/10.54 apply zenon_Ha8. apply refl_equal. % 10.36/10.54 (* end of lemma zenon_L789_ *) % 10.36/10.54 assert (zenon_L790_ : ((op (e3) (e1)) = (e2)) -> ((op (e1) (e0)) = (e3)) -> ((op (e1) (e1)) = (e0)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H252 zenon_H13c zenon_H6f. % 10.36/10.54 apply (zenon_notand_s _ _ ax13); [ zenon_intro zenon_H314 | zenon_intro zenon_H315 ]. % 10.36/10.54 apply zenon_H314. apply sym_equal. exact zenon_H6f. % 10.36/10.54 apply (zenon_notand_s _ _ zenon_H315); [ zenon_intro zenon_H2c1 | zenon_intro zenon_Ha6 ]. % 10.36/10.54 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.36/10.54 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((e3) = (op (e1) (op (e1) (e1))))). % 10.36/10.54 intro zenon_D_pnotp. % 10.36/10.54 apply zenon_H2c1. % 10.36/10.54 rewrite <- zenon_D_pnotp. % 10.36/10.54 exact zenon_Hae. % 10.36/10.54 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.36/10.54 cut (((op (e1) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 10.36/10.54 congruence. % 10.36/10.54 cut (((op (e1) (e0)) = (e3)) = ((op (e1) (op (e1) (e1))) = (e3))). % 10.36/10.54 intro zenon_D_pnotp. % 10.36/10.54 apply zenon_H2c2. % 10.36/10.54 rewrite <- zenon_D_pnotp. % 10.36/10.54 exact zenon_H13c. % 10.36/10.54 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 10.36/10.54 cut (((op (e1) (e0)) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H312]. % 10.36/10.54 congruence. % 10.36/10.54 elim (classic ((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 10.36/10.54 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1)))) = ((op (e1) (e0)) = (op (e1) (op (e1) (e1))))). % 10.36/10.54 intro zenon_D_pnotp. % 10.36/10.54 apply zenon_H312. % 10.36/10.54 rewrite <- zenon_D_pnotp. % 10.36/10.54 exact zenon_Hae. % 10.36/10.54 cut (((op (e1) (op (e1) (e1))) = (op (e1) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 10.36/10.54 cut (((op (e1) (op (e1) (e1))) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H311]. % 10.36/10.54 congruence. % 10.36/10.54 apply (zenon_L763_); trivial. % 10.36/10.54 apply zenon_Haf. apply refl_equal. % 10.36/10.54 apply zenon_Haf. apply refl_equal. % 10.36/10.54 apply zenon_Heb. apply refl_equal. % 10.36/10.54 apply zenon_Haf. apply refl_equal. % 10.36/10.54 apply zenon_Haf. apply refl_equal. % 10.36/10.54 apply (zenon_L789_); trivial. % 10.36/10.54 (* end of lemma zenon_L790_ *) % 10.36/10.54 assert (zenon_L791_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e0))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H245 zenon_H13b zenon_He9 zenon_H6f zenon_H262 zenon_H42 zenon_H27c zenon_H76. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.54 apply (zenon_L575_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.54 apply (zenon_L767_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.54 apply (zenon_L322_); trivial. % 10.36/10.54 exact (zenon_H76 zenon_H79). % 10.36/10.54 (* end of lemma zenon_L791_ *) % 10.36/10.54 assert (zenon_L792_ : (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H2f2 zenon_H262 zenon_Hf6 zenon_H14b zenon_H6f zenon_H13c zenon_H120 zenon_H154. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2f2); [ zenon_intro zenon_H128 | zenon_intro zenon_H2f3 ]. % 10.36/10.54 apply (zenon_L767_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H175 | zenon_intro zenon_H2f4 ]. % 10.36/10.54 apply (zenon_L124_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H252 | zenon_intro zenon_H127 ]. % 10.36/10.54 apply (zenon_L790_); trivial. % 10.36/10.54 apply (zenon_L93_); trivial. % 10.36/10.54 (* end of lemma zenon_L792_ *) % 10.36/10.54 assert (zenon_L793_ : (((op (e2) (e1)) = (e0))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e1)) = (e2))\/((op (e2) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H2d6 zenon_H171 zenon_H100 zenon_H51 zenon_H2a5 zenon_H2f2 zenon_H262 zenon_Hf6 zenon_H14b zenon_H6f zenon_H13c zenon_H154. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H2d7 ]. % 10.36/10.54 apply (zenon_L762_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H101 | zenon_intro zenon_H2d8 ]. % 10.36/10.54 apply (zenon_L61_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2d8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H120 ]. % 10.36/10.54 apply (zenon_L287_); trivial. % 10.36/10.54 apply (zenon_L792_); trivial. % 10.36/10.54 (* end of lemma zenon_L793_ *) % 10.36/10.54 assert (zenon_L794_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H2b9 zenon_H31 zenon_H152 zenon_H8c zenon_H101 zenon_Hf4 zenon_Hfd zenon_H127. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.54 apply (zenon_L301_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.54 exact (zenon_H8c zenon_H91). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.54 apply (zenon_L193_); trivial. % 10.36/10.54 apply (zenon_L199_); trivial. % 10.36/10.54 (* end of lemma zenon_L794_ *) % 10.36/10.54 assert (zenon_L795_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H28c zenon_H1f zenon_Hc0 zenon_H136 zenon_H135 zenon_H2b9 zenon_H31 zenon_H8c zenon_H101 zenon_Hf4 zenon_Hfd zenon_H127. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H28d ]. % 10.36/10.54 apply (zenon_L44_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_Hfa | zenon_intro zenon_H28e ]. % 10.36/10.54 apply (zenon_L121_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H152 ]. % 10.36/10.54 apply (zenon_L83_); trivial. % 10.36/10.54 apply (zenon_L794_); trivial. % 10.36/10.54 (* end of lemma zenon_L795_ *) % 10.36/10.54 assert (zenon_L796_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e0)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H2db zenon_Hf4 zenon_H101 zenon_H8c zenon_H31 zenon_H2b9 zenon_H135 zenon_Hc0 zenon_H1f zenon_H28c zenon_H127 zenon_Hfd zenon_H51 zenon_H278 zenon_H1ee. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H136 | zenon_intro zenon_H2dc ]. % 10.36/10.54 apply (zenon_L795_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H252 | zenon_intro zenon_H2dd ]. % 10.36/10.54 apply (zenon_L199_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H2d9 | zenon_intro zenon_Hd3 ]. % 10.36/10.54 apply (zenon_L754_); trivial. % 10.36/10.54 exact (zenon_H1ee zenon_Hd3). % 10.36/10.54 (* end of lemma zenon_L796_ *) % 10.36/10.54 assert (zenon_L797_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e1) (e1)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e2)) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hdf zenon_Hfd zenon_H6f zenon_He9 zenon_Hf6 zenon_H104 zenon_H12a zenon_H2a5 zenon_H177 zenon_Hf4 zenon_H2b9 zenon_H8c zenon_H182 zenon_H51 zenon_H24b zenon_He5. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.54 apply (zenon_L777_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.54 exact (zenon_H8c zenon_H91). % 10.36/10.54 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.54 apply (zenon_L307_); trivial. % 10.36/10.54 apply (zenon_L213_); trivial. % 10.36/10.54 (* end of lemma zenon_L797_ *) % 10.36/10.54 assert (zenon_L798_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H2b9 zenon_H31 zenon_H287 zenon_H51 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_H8c zenon_Hc4 zenon_H85 zenon_Hfd zenon_H127. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.54 apply (zenon_L302_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.54 exact (zenon_H8c zenon_H91). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.54 apply (zenon_L45_); trivial. % 10.36/10.54 apply (zenon_L199_); trivial. % 10.36/10.54 (* end of lemma zenon_L798_ *) % 10.36/10.54 assert (zenon_L799_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H3e zenon_H42 zenon_H2e4. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H2d. zenon_intro zenon_H3f. % 10.36/10.54 apply (zenon_L494_); trivial. % 10.36/10.54 (* end of lemma zenon_L799_ *) % 10.36/10.54 assert (zenon_L800_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> ((op (e1) (e2)) = (e1)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H4b zenon_H8b. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H42. zenon_intro zenon_H4c. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H44. zenon_intro zenon_H8f. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.36/10.54 exact (zenon_H90 zenon_H8b). % 10.36/10.54 (* end of lemma zenon_L800_ *) % 10.36/10.54 assert (zenon_L801_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H52 zenon_H1ed. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H42. zenon_intro zenon_H53. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H44. zenon_intro zenon_H1c8. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.36/10.54 exact (zenon_H1f9 zenon_H1ed). % 10.36/10.54 (* end of lemma zenon_L801_ *) % 10.36/10.54 assert (zenon_L802_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H5f zenon_H42 zenon_H284. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H56. zenon_intro zenon_H60. % 10.36/10.54 apply (zenon_L619_); trivial. % 10.36/10.54 (* end of lemma zenon_L802_ *) % 10.36/10.54 assert (zenon_L803_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H61 zenon_H42 zenon_H284. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H56. zenon_intro zenon_H62. % 10.36/10.54 apply (zenon_L619_); trivial. % 10.36/10.54 (* end of lemma zenon_L803_ *) % 10.36/10.54 assert (zenon_L804_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H75 zenon_H8b zenon_H18d. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H6a. zenon_intro zenon_H77. % 10.36/10.54 apply (zenon_L128_); trivial. % 10.36/10.54 (* end of lemma zenon_L804_ *) % 10.36/10.54 assert (zenon_L805_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e0) (e2)) = (e0)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H89 zenon_H42. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8c. zenon_intro zenon_H43. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.36/10.54 exact (zenon_H45 zenon_H42). % 10.36/10.54 (* end of lemma zenon_L805_ *) % 10.36/10.54 assert (zenon_L806_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3)))))) -> ((op (e3) (e2)) = (e3)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H18f zenon_H1ed. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H8b. zenon_intro zenon_H190. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H190). zenon_intro zenon_H8c. zenon_intro zenon_H1c8. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.36/10.54 exact (zenon_H1f9 zenon_H1ed). % 10.36/10.54 (* end of lemma zenon_L806_ *) % 10.36/10.54 assert (zenon_L807_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hef zenon_H8b zenon_H316. % 10.36/10.54 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H116 | zenon_intro zenon_Hc9 ]. % 10.36/10.54 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e1) (e2)) = (op (e1) (e3)))). % 10.36/10.54 intro zenon_D_pnotp. % 10.36/10.54 apply zenon_H316. % 10.36/10.54 rewrite <- zenon_D_pnotp. % 10.36/10.54 exact zenon_H116. % 10.36/10.54 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 10.36/10.54 cut (((op (e1) (e3)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H317]. % 10.36/10.54 congruence. % 10.36/10.54 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e1) (e2)))). % 10.36/10.54 intro zenon_D_pnotp. % 10.36/10.54 apply zenon_H317. % 10.36/10.54 rewrite <- zenon_D_pnotp. % 10.36/10.54 exact zenon_Hef. % 10.36/10.54 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 10.36/10.54 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 10.36/10.54 congruence. % 10.36/10.54 apply zenon_Hc9. apply refl_equal. % 10.36/10.54 apply zenon_H184. apply sym_equal. exact zenon_H8b. % 10.36/10.54 apply zenon_Hc9. apply refl_equal. % 10.36/10.54 apply zenon_Hc9. apply refl_equal. % 10.36/10.54 (* end of lemma zenon_L807_ *) % 10.36/10.54 assert (zenon_L808_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hed zenon_H8b zenon_H316. % 10.36/10.54 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hef. zenon_intro zenon_Hee. % 10.36/10.54 apply (zenon_L807_); trivial. % 10.36/10.54 (* end of lemma zenon_L808_ *) % 10.36/10.54 assert (zenon_L809_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H16f zenon_H8b zenon_H316. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hef. zenon_intro zenon_H170. % 10.36/10.54 apply (zenon_L807_); trivial. % 10.36/10.54 (* end of lemma zenon_L809_ *) % 10.36/10.54 assert (zenon_L810_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1d8 zenon_H1ed zenon_H1ef. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1d8). zenon_intro zenon_H13b. zenon_intro zenon_H1d9. % 10.36/10.54 apply (zenon_L176_); trivial. % 10.36/10.54 (* end of lemma zenon_L810_ *) % 10.36/10.54 assert (zenon_L811_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1da zenon_H42 zenon_Hce. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_H13b. zenon_intro zenon_H1db. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1db). zenon_intro zenon_H76. zenon_intro zenon_H27. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.36/10.54 apply (zenon_L677_); trivial. % 10.36/10.54 (* end of lemma zenon_L811_ *) % 10.36/10.54 assert (zenon_L812_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1e1 zenon_H1ed zenon_H2ef. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H127. zenon_intro zenon_H1e2. % 10.36/10.54 apply (zenon_L530_); trivial. % 10.36/10.54 (* end of lemma zenon_L812_ *) % 10.36/10.54 assert (zenon_L813_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1e6 zenon_H8b zenon_H182. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H127. zenon_intro zenon_H1e7. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1e5. zenon_intro zenon_H80. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.36/10.54 apply (zenon_L122_); trivial. % 10.36/10.54 (* end of lemma zenon_L813_ *) % 10.36/10.54 assert (zenon_L814_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e0) (e2)) = (e0)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1eb zenon_H42. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ed. zenon_intro zenon_H1ec. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ee. zenon_intro zenon_H43. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.36/10.54 exact (zenon_H45 zenon_H42). % 10.36/10.54 (* end of lemma zenon_L814_ *) % 10.36/10.54 assert (zenon_L815_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> ((op (e1) (e2)) = (e1)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1f3 zenon_H8b. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H1ed. zenon_intro zenon_H1f4. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1f4). zenon_intro zenon_H1ee. zenon_intro zenon_H8f. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.36/10.54 exact (zenon_H90 zenon_H8b). % 10.36/10.54 (* end of lemma zenon_L815_ *) % 10.36/10.54 assert (zenon_L816_ : ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H202 zenon_Hf4 zenon_H2e4 zenon_H284 zenon_H85 zenon_H18d zenon_H316 zenon_H287 zenon_H2a5 zenon_H51 zenon_H28f zenon_H1ef zenon_Hce zenon_H2ef zenon_H1ed zenon_H182 zenon_H42 zenon_H8b. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.54 apply (zenon_L1_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.54 apply (zenon_L2_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.54 apply (zenon_L3_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.54 apply (zenon_L4_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.54 apply (zenon_L5_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.54 apply (zenon_L6_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.54 apply (zenon_L744_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.54 apply (zenon_L799_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.54 apply (zenon_L10_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.54 apply (zenon_L800_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.54 apply (zenon_L13_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.54 apply (zenon_L801_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.54 apply (zenon_L15_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.54 apply (zenon_L802_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.54 apply (zenon_L803_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.54 apply (zenon_L19_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.54 apply (zenon_L20_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.54 apply (zenon_L21_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.54 apply (zenon_L757_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.54 apply (zenon_L804_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.54 apply (zenon_L24_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.54 apply (zenon_L25_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.54 apply (zenon_L26_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.54 apply (zenon_L27_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.54 apply (zenon_L805_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.54 apply (zenon_L31_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.54 apply (zenon_L32_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.54 apply (zenon_L806_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.54 apply (zenon_L808_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.54 apply (zenon_L56_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.54 apply (zenon_L809_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.54 apply (zenon_L147_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.54 apply (zenon_L148_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.54 apply (zenon_L785_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.54 apply (zenon_L150_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.54 apply (zenon_L672_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.54 apply (zenon_L786_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.54 apply (zenon_L154_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.54 apply (zenon_L155_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.54 apply (zenon_L288_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.54 apply (zenon_L157_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.54 apply (zenon_L158_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.54 apply (zenon_L159_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.54 apply (zenon_L160_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.54 apply (zenon_L679_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.54 apply (zenon_L265_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.54 apply (zenon_L164_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.54 apply (zenon_L165_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.54 apply (zenon_L166_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.54 apply (zenon_L810_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.54 apply (zenon_L811_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.54 apply (zenon_L169_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.54 apply (zenon_L812_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.54 apply (zenon_L172_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.54 apply (zenon_L813_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.54 apply (zenon_L174_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.54 apply (zenon_L814_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.54 apply (zenon_L815_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.54 apply (zenon_L178_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.54 apply (zenon_L179_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.54 apply (zenon_L180_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.54 apply (zenon_L181_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.54 apply (zenon_L182_); trivial. % 10.36/10.54 apply (zenon_L183_); trivial. % 10.36/10.54 (* end of lemma zenon_L816_ *) % 10.36/10.54 assert (zenon_L817_ : (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H318 zenon_H27c zenon_H186 zenon_H278 zenon_H202 zenon_Hf4 zenon_H2e4 zenon_H284 zenon_H85 zenon_H18d zenon_H316 zenon_H287 zenon_H2a5 zenon_H51 zenon_H28f zenon_H1ef zenon_Hce zenon_H2ef zenon_H182 zenon_H42 zenon_H8b. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H241 | zenon_intro zenon_H319 ]. % 10.36/10.54 apply (zenon_L322_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H187 | zenon_intro zenon_H31a ]. % 10.36/10.54 apply (zenon_L125_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H2d9 | zenon_intro zenon_H1ed ]. % 10.36/10.54 apply (zenon_L754_); trivial. % 10.36/10.54 apply (zenon_L816_); trivial. % 10.36/10.54 (* end of lemma zenon_L817_ *) % 10.36/10.54 assert (zenon_L818_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H15e zenon_H104 zenon_H31 zenon_H136 zenon_He9 zenon_H42 zenon_He5 zenon_Hfd. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.54 apply (zenon_L295_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.54 apply (zenon_L202_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.54 apply (zenon_L616_); trivial. % 10.36/10.54 apply (zenon_L103_); trivial. % 10.36/10.54 (* end of lemma zenon_L818_ *) % 10.36/10.54 assert (zenon_L819_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H2c5 zenon_Hfd zenon_H42 zenon_He9 zenon_H136 zenon_H31 zenon_H104 zenon_H15e zenon_Hf4 zenon_Hef zenon_H51 zenon_H28f zenon_H1ee. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.36/10.54 apply (zenon_L818_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.36/10.54 apply (zenon_L97_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.36/10.54 apply (zenon_L264_); trivial. % 10.36/10.54 exact (zenon_H1ee zenon_Hd3). % 10.36/10.54 (* end of lemma zenon_L819_ *) % 10.36/10.54 assert (zenon_L820_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H2ab zenon_H13c zenon_H99 zenon_H6f zenon_H182 zenon_H2ef zenon_Hce zenon_H1ef zenon_H2a5 zenon_H287 zenon_H316 zenon_H18d zenon_H85 zenon_H284 zenon_H2e4 zenon_H202 zenon_H278 zenon_H186 zenon_H27c zenon_H318 zenon_H2c5 zenon_Hfd zenon_H42 zenon_He9 zenon_H136 zenon_H31 zenon_H104 zenon_H15e zenon_Hf4 zenon_H51 zenon_H28f zenon_H1ee. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.36/10.54 apply (zenon_L248_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.36/10.54 apply (zenon_L312_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.36/10.54 apply (zenon_L817_); trivial. % 10.36/10.54 apply (zenon_L819_); trivial. % 10.36/10.54 (* end of lemma zenon_L820_ *) % 10.36/10.54 assert (zenon_L821_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> ((op (e1) (e0)) = (e3)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H12d zenon_H30 zenon_H1ee zenon_H28f zenon_H51 zenon_Hf4 zenon_H15e zenon_H104 zenon_H31 zenon_H136 zenon_H42 zenon_Hfd zenon_H2c5 zenon_H318 zenon_H27c zenon_H186 zenon_H278 zenon_H202 zenon_H2e4 zenon_H284 zenon_H85 zenon_H18d zenon_H316 zenon_H287 zenon_H2a5 zenon_H1ef zenon_Hce zenon_H2ef zenon_H182 zenon_H99 zenon_H13c zenon_H2ab zenon_Hc1 zenon_H1b2 zenon_He9 zenon_H127. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.54 exact (zenon_H30 zenon_H2d). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.54 apply (zenon_L820_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.54 apply (zenon_L259_); trivial. % 10.36/10.54 apply (zenon_L77_); trivial. % 10.36/10.54 (* end of lemma zenon_L821_ *) % 10.36/10.54 assert (zenon_L822_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> ((op (e3) (e0)) = (e2)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H289 zenon_H135 zenon_H136 zenon_Hc0 zenon_H12d zenon_H30 zenon_H1ee zenon_H28f zenon_H51 zenon_Hf4 zenon_H15e zenon_H104 zenon_H42 zenon_Hfd zenon_H2c5 zenon_H318 zenon_H27c zenon_H186 zenon_H278 zenon_H202 zenon_H2e4 zenon_H284 zenon_H85 zenon_H18d zenon_H316 zenon_H287 zenon_H2a5 zenon_H1ef zenon_Hce zenon_H2ef zenon_H182 zenon_H99 zenon_H2ab zenon_H1b2 zenon_He9 zenon_H28c zenon_H31 zenon_Ha4 zenon_H127 zenon_H1de. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.54 apply (zenon_L295_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28c); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H28d ]. % 10.36/10.54 apply (zenon_L821_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_Hfa | zenon_intro zenon_H28e ]. % 10.36/10.54 apply (zenon_L121_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H152 ]. % 10.36/10.54 apply (zenon_L83_); trivial. % 10.36/10.54 apply (zenon_L301_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.54 apply (zenon_L301_); trivial. % 10.36/10.54 apply (zenon_L170_); trivial. % 10.36/10.54 (* end of lemma zenon_L822_ *) % 10.36/10.54 assert (zenon_L823_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H15e zenon_H104 zenon_H31 zenon_H14b zenon_H127 zenon_He9 zenon_H42 zenon_He5 zenon_Hfd. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.54 apply (zenon_L295_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.54 apply (zenon_L90_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.54 apply (zenon_L616_); trivial. % 10.36/10.54 apply (zenon_L103_); trivial. % 10.36/10.54 (* end of lemma zenon_L823_ *) % 10.36/10.54 assert (zenon_L824_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e1)) = (e0))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e2) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1a3 zenon_H1ee zenon_H278 zenon_H289 zenon_H135 zenon_Hc0 zenon_H12d zenon_H30 zenon_H28f zenon_Hf4 zenon_H2c5 zenon_H318 zenon_H27c zenon_H186 zenon_H202 zenon_H2e4 zenon_H284 zenon_H85 zenon_H18d zenon_H316 zenon_H287 zenon_H2a5 zenon_H1ef zenon_H2ef zenon_H182 zenon_H99 zenon_H2ab zenon_H1b2 zenon_H28c zenon_H1de zenon_H2db zenon_Hce zenon_H51 zenon_H15e zenon_H104 zenon_H31 zenon_H14b zenon_H127 zenon_He9 zenon_H42 zenon_Hfd. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.54 apply (zenon_L57_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H136 | zenon_intro zenon_H2dc ]. % 10.36/10.54 apply (zenon_L822_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H252 | zenon_intro zenon_H2dd ]. % 10.36/10.54 apply (zenon_L199_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H2d9 | zenon_intro zenon_Hd3 ]. % 10.36/10.54 apply (zenon_L754_); trivial. % 10.36/10.54 exact (zenon_H1ee zenon_Hd3). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.54 apply (zenon_L48_); trivial. % 10.36/10.54 apply (zenon_L823_); trivial. % 10.36/10.54 (* end of lemma zenon_L824_ *) % 10.36/10.54 assert (zenon_L825_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H2c5 zenon_H85 zenon_H56 zenon_Hf4 zenon_Hef zenon_H51 zenon_H28f zenon_H1ee. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.36/10.54 apply (zenon_L663_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.36/10.54 apply (zenon_L97_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.36/10.54 apply (zenon_L264_); trivial. % 10.36/10.54 exact (zenon_H1ee zenon_Hd3). % 10.36/10.54 (* end of lemma zenon_L825_ *) % 10.36/10.54 assert (zenon_L826_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e1)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H2ab zenon_H94 zenon_H99 zenon_H6f zenon_H1e5 zenon_H186 zenon_H104 zenon_H127 zenon_H130 zenon_H31 zenon_H18a zenon_H2c5 zenon_H85 zenon_H56 zenon_Hf4 zenon_H51 zenon_H28f zenon_H1ee. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.36/10.54 apply (zenon_L115_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.36/10.54 apply (zenon_L312_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.36/10.54 apply (zenon_L296_); trivial. % 10.36/10.54 apply (zenon_L825_); trivial. % 10.36/10.54 (* end of lemma zenon_L826_ *) % 10.36/10.54 assert (zenon_L827_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (~((op (e0) (e0)) = (e2))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1eb zenon_H44. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ed. zenon_intro zenon_H1ec. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ee. zenon_intro zenon_H43. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.36/10.54 exact (zenon_H44 zenon_H46). % 10.36/10.54 (* end of lemma zenon_L827_ *) % 10.36/10.54 assert (zenon_L828_ : (((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (~((op (e1) (e1)) = (e2))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H1f3 zenon_H8c. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H1ed. zenon_intro zenon_H1f4. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H1f4). zenon_intro zenon_H1ee. zenon_intro zenon_H8f. % 10.36/10.54 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.36/10.54 exact (zenon_H8c zenon_H91). % 10.36/10.54 (* end of lemma zenon_L828_ *) % 10.36/10.54 assert (zenon_L829_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H281 zenon_H44 zenon_Hf4 zenon_H51 zenon_H287 zenon_H289 zenon_H58 zenon_H104 zenon_H6a zenon_He9 zenon_Hc1 zenon_Hfd. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.54 exact (zenon_H44 zenon_H46). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.54 apply (zenon_L236_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.54 apply (zenon_L299_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.54 exact (zenon_H58 zenon_H5a). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.54 apply (zenon_L248_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.54 apply (zenon_L658_); trivial. % 10.36/10.54 apply (zenon_L255_); trivial. % 10.36/10.54 (* end of lemma zenon_L829_ *) % 10.36/10.54 assert (zenon_L830_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H303 zenon_H5b zenon_H56 zenon_Hfa zenon_Hc0 zenon_H44 zenon_H58. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H1f | zenon_intro zenon_H304 ]. % 10.36/10.54 apply (zenon_L16_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H31 | zenon_intro zenon_H305 ]. % 10.36/10.54 apply (zenon_L121_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H46 | zenon_intro zenon_H5a ]. % 10.36/10.54 exact (zenon_H44 zenon_H46). % 10.36/10.54 exact (zenon_H58 zenon_H5a). % 10.36/10.54 (* end of lemma zenon_L830_ *) % 10.36/10.54 assert (zenon_L831_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e3) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H303 zenon_Hc1 zenon_Hc0 zenon_H133 zenon_H130 zenon_H44 zenon_H58. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H1f | zenon_intro zenon_H304 ]. % 10.36/10.54 apply (zenon_L44_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H31 | zenon_intro zenon_H305 ]. % 10.36/10.54 apply (zenon_L82_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H46 | zenon_intro zenon_H5a ]. % 10.36/10.54 exact (zenon_H44 zenon_H46). % 10.36/10.54 exact (zenon_H58 zenon_H5a). % 10.36/10.54 (* end of lemma zenon_L831_ *) % 10.36/10.54 assert (zenon_L832_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H191 zenon_H85 zenon_Hce zenon_H177 zenon_Ha2 zenon_H1ed zenon_H1ef zenon_H1a3 zenon_Hfd zenon_He9 zenon_H104 zenon_H289 zenon_H287 zenon_H51 zenon_Hf4 zenon_H281 zenon_H56 zenon_H5b zenon_H303 zenon_Hc1 zenon_Hc0 zenon_H130 zenon_H44 zenon_H58. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.54 exact (zenon_H44 zenon_H46). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.54 exact (zenon_H58 zenon_H5a). % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.54 apply (zenon_L116_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.54 apply (zenon_L301_); trivial. % 10.36/10.54 apply (zenon_L176_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.54 apply (zenon_L48_); trivial. % 10.36/10.54 apply (zenon_L663_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.54 apply (zenon_L829_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.54 apply (zenon_L830_); trivial. % 10.36/10.54 apply (zenon_L831_); trivial. % 10.36/10.54 (* end of lemma zenon_L832_ *) % 10.36/10.54 assert (zenon_L833_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hb6 zenon_H6a zenon_H6b zenon_H1ed zenon_H104 zenon_H51 zenon_Hf4 zenon_H99 zenon_H198 zenon_H284 zenon_H293 zenon_H79 zenon_H29d. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.36/10.54 apply (zenon_L394_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.36/10.54 exact (zenon_H6b zenon_H6f). % 10.36/10.54 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.36/10.54 apply (zenon_L585_); trivial. % 10.36/10.54 apply (zenon_L579_); trivial. % 10.36/10.54 (* end of lemma zenon_L833_ *) % 10.36/10.54 assert (zenon_L834_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> False). % 10.36/10.54 do 0 intro. intros zenon_H269 zenon_H5b zenon_H1f zenon_H107 zenon_H157 zenon_Hdd zenon_H24b zenon_H17c. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H56 | zenon_intro zenon_H26a ]. % 10.36/10.54 apply (zenon_L16_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H198 | zenon_intro zenon_H26b ]. % 10.36/10.54 apply (zenon_L210_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_He5 | zenon_intro zenon_H158 ]. % 10.36/10.54 apply (zenon_L213_); trivial. % 10.36/10.54 apply (zenon_L253_); trivial. % 10.36/10.54 (* end of lemma zenon_L834_ *) % 10.36/10.54 assert (zenon_L835_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H298 zenon_H29d zenon_H293 zenon_H284 zenon_H51 zenon_H104 zenon_H1ed zenon_H6b zenon_H6a zenon_Hb6 zenon_Hf4 zenon_H17c zenon_H24b zenon_Hdd zenon_H157 zenon_H1f zenon_H5b zenon_H269 zenon_H79 zenon_H99. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.36/10.54 apply (zenon_L833_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.36/10.54 apply (zenon_L97_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.36/10.54 apply (zenon_L834_); trivial. % 10.36/10.54 apply (zenon_L273_); trivial. % 10.36/10.54 (* end of lemma zenon_L835_ *) % 10.36/10.54 assert (zenon_L836_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 10.36/10.54 do 0 intro. intros zenon_Hda zenon_H42 zenon_H9a. % 10.36/10.54 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 10.36/10.54 intro zenon_D_pnotp. % 10.36/10.54 apply zenon_Hda. % 10.36/10.54 rewrite <- zenon_D_pnotp. % 10.36/10.54 exact zenon_H42. % 10.36/10.54 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H31b]. % 10.36/10.54 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 10.36/10.54 congruence. % 10.36/10.54 apply zenon_H49. apply refl_equal. % 10.36/10.54 apply zenon_H31b. apply sym_equal. exact zenon_H9a. % 10.36/10.54 (* end of lemma zenon_L836_ *) % 10.36/10.54 assert (zenon_L837_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 10.36/10.54 do 0 intro. intros zenon_H31c zenon_H42 zenon_Hda zenon_H187 zenon_H182 zenon_H51 zenon_H1ed zenon_H186. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H31c); [ zenon_intro zenon_H9a | zenon_intro zenon_H31d ]. % 10.36/10.54 apply (zenon_L836_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H31d); [ zenon_intro zenon_H8b | zenon_intro zenon_H31e ]. % 10.36/10.54 apply (zenon_L125_); trivial. % 10.36/10.54 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_Hdb | zenon_intro zenon_H17a ]. % 10.36/10.54 apply (zenon_L307_); trivial. % 10.36/10.54 apply (zenon_L249_); trivial. % 10.36/10.54 (* end of lemma zenon_L837_ *) % 10.36/10.54 assert (zenon_L838_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H293 zenon_H99 zenon_H18d zenon_H6a zenon_Hf4 zenon_H31c zenon_H42 zenon_Hda zenon_H182 zenon_H51 zenon_H1ed zenon_H186. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.36/10.55 apply (zenon_L421_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.36/10.55 apply (zenon_L128_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.36/10.55 apply (zenon_L328_); trivial. % 10.36/10.55 apply (zenon_L837_); trivial. % 10.36/10.55 (* end of lemma zenon_L838_ *) % 10.36/10.55 assert (zenon_L839_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e2))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H75 zenon_H293 zenon_H99 zenon_H18d zenon_Hf4 zenon_H31c zenon_H42 zenon_Hda zenon_H182 zenon_H51 zenon_H1ed zenon_H186. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H6a. zenon_intro zenon_H77. % 10.36/10.55 apply (zenon_L838_); trivial. % 10.36/10.55 (* end of lemma zenon_L839_ *) % 10.36/10.55 assert (zenon_L840_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H17e zenon_H5a zenon_H94 zenon_Ha3 zenon_H186 zenon_H1ed zenon_Hef zenon_H104. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.55 apply (zenon_L359_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.55 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.55 apply (zenon_L249_); trivial. % 10.36/10.55 apply (zenon_L341_); trivial. % 10.36/10.55 (* end of lemma zenon_L840_ *) % 10.36/10.55 assert (zenon_L841_ : ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H202 zenon_H26e zenon_H15e zenon_H27c zenon_Hca zenon_H130 zenon_H281 zenon_H289 zenon_He9 zenon_H177 zenon_H191 zenon_H28c zenon_H1b2 zenon_Hc0 zenon_H303 zenon_He6 zenon_H293 zenon_H99 zenon_H18d zenon_H31c zenon_Hda zenon_H182 zenon_H1a3 zenon_Hce zenon_Hdf zenon_H24b zenon_H12d zenon_H37 zenon_H269 zenon_H5b zenon_H157 zenon_Hb6 zenon_H284 zenon_H29d zenon_H298 zenon_H2ed zenon_H308 zenon_H104 zenon_H186 zenon_H94 zenon_H17e zenon_Hfd zenon_H287 zenon_H2a5 zenon_H28f zenon_H1ef zenon_H85 zenon_H2ef zenon_H1ed zenon_Hf4 zenon_H51 zenon_H44 zenon_H8c. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.55 apply (zenon_L1_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.55 apply (zenon_L2_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.55 apply (zenon_L3_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.55 apply (zenon_L4_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.55 apply (zenon_L5_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.55 apply (zenon_L6_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.55 apply (zenon_L744_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H2d. zenon_intro zenon_H3f. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H2f. zenon_intro zenon_H83. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.36/10.55 apply (zenon_L749_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.55 apply (zenon_L10_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.55 apply (zenon_L750_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.55 apply (zenon_L13_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.55 apply (zenon_L801_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.55 apply (zenon_L15_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H56. zenon_intro zenon_H60. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H58. zenon_intro zenon_Hf2. % 10.36/10.55 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.55 exact (zenon_H44 zenon_H46). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.36/10.55 apply (zenon_L832_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.36/10.55 apply (zenon_L752_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.36/10.55 apply (zenon_L595_); trivial. % 10.36/10.55 apply (zenon_L209_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.55 apply (zenon_L48_); trivial. % 10.36/10.55 apply (zenon_L663_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.55 apply (zenon_L666_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.55 apply (zenon_L19_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.55 apply (zenon_L20_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.55 apply (zenon_L21_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.55 apply (zenon_L757_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H6a. zenon_intro zenon_H77. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H6b. zenon_intro zenon_H2a. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.55 apply (zenon_L7_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.55 exact (zenon_H6b zenon_H6f). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.55 apply (zenon_L236_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.55 exact (zenon_H8c zenon_H91). % 10.36/10.55 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.55 apply (zenon_L307_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.55 apply (zenon_L248_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.55 apply (zenon_L137_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.55 apply (zenon_L249_); trivial. % 10.36/10.55 apply (zenon_L835_); trivial. % 10.36/10.55 apply (zenon_L525_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.55 apply (zenon_L747_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.55 apply (zenon_L839_); trivial. % 10.36/10.55 apply (zenon_L584_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.55 apply (zenon_L24_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.55 apply (zenon_L25_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.55 apply (zenon_L26_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.55 apply (zenon_L27_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.55 apply (zenon_L759_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.55 apply (zenon_L31_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.55 apply (zenon_L32_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.55 apply (zenon_L806_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.55 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hef. zenon_intro zenon_Hee. % 10.36/10.55 apply (zenon_and_s _ _ zenon_Hee). zenon_intro zenon_Ha3. zenon_intro zenon_H57. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.36/10.55 apply (zenon_L840_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.55 apply (zenon_L56_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.55 apply (zenon_L784_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.55 apply (zenon_L147_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.55 apply (zenon_L148_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.55 apply (zenon_L785_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.55 apply (zenon_L150_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.55 apply (zenon_L672_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.55 apply (zenon_L786_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.55 apply (zenon_L154_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.55 apply (zenon_L155_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.55 apply (zenon_L288_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.55 apply (zenon_L157_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.55 apply (zenon_L158_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.55 apply (zenon_L159_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.55 apply (zenon_L160_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.55 apply (zenon_L679_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.55 apply (zenon_L265_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.55 apply (zenon_L164_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.55 apply (zenon_L165_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.55 apply (zenon_L166_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.55 apply (zenon_L810_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.55 apply (zenon_L710_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.55 apply (zenon_L169_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.55 apply (zenon_L812_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.55 apply (zenon_L172_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.55 apply (zenon_L484_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.55 apply (zenon_L174_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.55 apply (zenon_L827_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.55 apply (zenon_L828_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.55 apply (zenon_L178_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.55 apply (zenon_L179_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.55 apply (zenon_L180_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.55 apply (zenon_L181_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.55 apply (zenon_L182_); trivial. % 10.36/10.55 apply (zenon_L183_); trivial. % 10.36/10.55 (* end of lemma zenon_L841_ *) % 10.36/10.55 assert (zenon_L842_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e1)) -> False). % 10.36/10.55 do 0 intro. intros zenon_H1a2 zenon_H2f zenon_H99 zenon_H2d zenon_Hda zenon_H8b zenon_He6 zenon_H189. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.55 exact (zenon_H2f zenon_H31). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.55 apply (zenon_L58_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.55 apply (zenon_L131_); trivial. % 10.36/10.55 apply (zenon_L140_); trivial. % 10.36/10.55 (* end of lemma zenon_L842_ *) % 10.36/10.55 assert (zenon_L843_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e0)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.55 do 0 intro. intros zenon_H18a zenon_H31 zenon_H130 zenon_H99 zenon_H128 zenon_H8b zenon_H186 zenon_H104 zenon_H67. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.36/10.55 apply (zenon_L82_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.36/10.55 apply (zenon_L111_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.36/10.55 apply (zenon_L125_); trivial. % 10.36/10.55 apply (zenon_L286_); trivial. % 10.36/10.55 (* end of lemma zenon_L843_ *) % 10.36/10.55 assert (zenon_L844_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H2bc zenon_H241 zenon_Hda zenon_H8b zenon_Hce zenon_H51 zenon_H1ed zenon_H27c. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H42 | zenon_intro zenon_H2bd ]. % 10.36/10.55 apply (zenon_L322_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H16e | zenon_intro zenon_H2be ]. % 10.36/10.55 apply (zenon_L131_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_Hcd | zenon_intro zenon_H150 ]. % 10.36/10.55 apply (zenon_L48_); trivial. % 10.36/10.55 apply (zenon_L252_); trivial. % 10.36/10.55 (* end of lemma zenon_L844_ *) % 10.36/10.55 assert (zenon_L845_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H2ae zenon_H284 zenon_H56 zenon_H99 zenon_H85 zenon_H2bc zenon_Hda zenon_H8b zenon_Hce zenon_H51 zenon_H1ed zenon_H27c. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.36/10.55 apply (zenon_L619_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.36/10.55 apply (zenon_L35_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.36/10.55 apply (zenon_L595_); trivial. % 10.36/10.55 apply (zenon_L844_); trivial. % 10.36/10.55 (* end of lemma zenon_L845_ *) % 10.36/10.55 assert (zenon_L846_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H5f zenon_H2ae zenon_H284 zenon_H99 zenon_H85 zenon_H2bc zenon_Hda zenon_H8b zenon_Hce zenon_H51 zenon_H1ed zenon_H27c. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H56. zenon_intro zenon_H60. % 10.36/10.55 apply (zenon_L845_); trivial. % 10.36/10.55 (* end of lemma zenon_L846_ *) % 10.36/10.55 assert (zenon_L847_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H1a3 zenon_H44 zenon_Hf4 zenon_Hf6 zenon_Hce zenon_H51 zenon_H56 zenon_H85. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.55 exact (zenon_H44 zenon_H46). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.55 apply (zenon_L89_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.55 apply (zenon_L48_); trivial. % 10.36/10.55 apply (zenon_L663_); trivial. % 10.36/10.55 (* end of lemma zenon_L847_ *) % 10.36/10.55 assert (zenon_L848_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e1) (e1)) = (e3)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H1a2 zenon_H12d zenon_Ha2 zenon_H287 zenon_Hc0 zenon_H1b2 zenon_H28c zenon_H2a8 zenon_H186 zenon_H130 zenon_H18a zenon_He9 zenon_H2db zenon_H14b zenon_H278 zenon_H1ee zenon_H244 zenon_H104 zenon_Hfd zenon_H5f zenon_H2ae zenon_H284 zenon_H2bc zenon_H27c zenon_H85 zenon_H51 zenon_Hce zenon_Hf4 zenon_H44 zenon_H1a3 zenon_Hda zenon_H8b zenon_H56 zenon_H99. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.55 exact (zenon_H44 zenon_H46). % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.55 apply (zenon_L486_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.55 apply (zenon_L776_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.55 apply (zenon_L302_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.36/10.55 apply (zenon_L755_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.36/10.55 apply (zenon_L77_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.36/10.55 apply (zenon_L252_); trivial. % 10.36/10.55 apply (zenon_L843_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.36/10.55 apply (zenon_L118_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.36/10.55 apply (zenon_L60_); trivial. % 10.36/10.55 apply (zenon_L846_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.55 apply (zenon_L48_); trivial. % 10.36/10.55 apply (zenon_L663_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.55 apply (zenon_L847_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.55 apply (zenon_L131_); trivial. % 10.36/10.55 apply (zenon_L670_); trivial. % 10.36/10.55 (* end of lemma zenon_L848_ *) % 10.36/10.55 assert (zenon_L849_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> False). % 10.36/10.55 do 0 intro. intros zenon_H18a zenon_H13b zenon_H104 zenon_H120 zenon_H100 zenon_H14b zenon_H252 zenon_H6f zenon_H173 zenon_H2e0 zenon_H8b zenon_H186 zenon_He6 zenon_H198. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.36/10.55 apply (zenon_L123_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.36/10.55 apply (zenon_L780_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.36/10.55 apply (zenon_L125_); trivial. % 10.36/10.55 apply (zenon_L140_); trivial. % 10.36/10.55 (* end of lemma zenon_L849_ *) % 10.36/10.55 assert (zenon_L850_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H15b zenon_H135 zenon_H186 zenon_H8b zenon_H2e0 zenon_H173 zenon_H6f zenon_H252 zenon_H14b zenon_H100 zenon_H104 zenon_H13b zenon_H18a zenon_Hfd zenon_H51 zenon_H2cf zenon_H76 zenon_H198 zenon_He6 zenon_H1ee zenon_Hd5. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.36/10.55 apply (zenon_L211_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.36/10.55 apply (zenon_L849_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.36/10.55 apply (zenon_L60_); trivial. % 10.36/10.55 apply (zenon_L398_); trivial. % 10.36/10.55 (* end of lemma zenon_L850_ *) % 10.36/10.55 assert (zenon_L851_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e0)) = (e1))\/(((op (e2) (e0)) = (e2))\/((op (e2) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e1)) = (e2))\/((op (e0) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H31f zenon_H318 zenon_H2e4 zenon_H1ef zenon_H2ef zenon_H182 zenon_H51 zenon_Hf4 zenon_H99 zenon_Hda zenon_H8b zenon_He6 zenon_H1a2 zenon_H1a3 zenon_H85 zenon_He9 zenon_H28c zenon_H287 zenon_Hc0 zenon_H1b2 zenon_H2a8 zenon_H2ae zenon_Hce zenon_H2bc zenon_H284 zenon_H2db zenon_H278 zenon_H14b zenon_Hfd zenon_H27c zenon_H18a zenon_H104 zenon_H186 zenon_H130 zenon_H244 zenon_H12d zenon_H44 zenon_H18d zenon_H316 zenon_H2a5 zenon_H28f zenon_H15b zenon_Hd5 zenon_H2cf zenon_H2e0 zenon_H100 zenon_H173 zenon_H2b9 zenon_H12a zenon_H177 zenon_H281 zenon_H135 zenon_H245 zenon_H262 zenon_H308 zenon_H202. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1ed ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.55 apply (zenon_L1_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.55 apply (zenon_L2_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.55 apply (zenon_L3_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.55 apply (zenon_L4_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.55 apply (zenon_L5_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.55 apply (zenon_L6_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.55 apply (zenon_L744_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H2d. zenon_intro zenon_H3f. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H2f. zenon_intro zenon_H83. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.36/10.55 apply (zenon_L842_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.55 apply (zenon_L10_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.55 apply (zenon_L800_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.55 apply (zenon_L13_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.55 apply (zenon_L751_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.55 apply (zenon_L15_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H56. zenon_intro zenon_H60. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H58. zenon_intro zenon_Hf2. % 10.36/10.55 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.36/10.55 apply (zenon_L848_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.55 apply (zenon_L666_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.55 apply (zenon_L19_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.55 apply (zenon_L20_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.55 apply (zenon_L21_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.55 apply (zenon_L757_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.55 apply (zenon_L804_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.55 apply (zenon_L24_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.55 apply (zenon_L25_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.55 apply (zenon_L26_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.55 apply (zenon_L27_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.55 apply (zenon_L759_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.55 apply (zenon_L31_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.55 apply (zenon_L32_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.55 apply (zenon_L760_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.55 apply (zenon_L808_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.55 apply (zenon_L56_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.55 apply (zenon_L784_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.55 apply (zenon_L147_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.55 apply (zenon_L148_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.55 apply (zenon_L785_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.55 apply (zenon_L150_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.55 apply (zenon_L672_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.55 apply (zenon_L786_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.55 apply (zenon_L154_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.55 apply (zenon_L155_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.55 apply (zenon_L288_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.55 apply (zenon_L157_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.55 apply (zenon_L158_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.55 apply (zenon_L159_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.55 apply (zenon_L160_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.55 apply (zenon_L679_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.55 apply (zenon_L265_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.55 apply (zenon_L164_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.55 apply (zenon_L165_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.55 apply (zenon_L166_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H1d8). zenon_intro zenon_H13b. zenon_intro zenon_H1d9. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H1d9). zenon_intro zenon_H76. zenon_intro zenon_H24. % 10.36/10.55 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.55 apply (zenon_L787_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.55 apply (zenon_L788_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.55 apply (zenon_L131_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.55 apply (zenon_L755_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.55 apply (zenon_L247_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.55 apply (zenon_L287_); trivial. % 10.36/10.55 apply (zenon_L850_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.55 apply (zenon_L504_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.55 apply (zenon_L791_); trivial. % 10.36/10.55 apply (zenon_L756_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.55 apply (zenon_L710_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.55 apply (zenon_L169_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.55 apply (zenon_L297_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.55 apply (zenon_L172_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.55 apply (zenon_L484_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.55 apply (zenon_L174_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.55 apply (zenon_L827_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.55 apply (zenon_L815_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.55 apply (zenon_L178_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.55 apply (zenon_L179_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.55 apply (zenon_L180_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.55 apply (zenon_L181_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.55 apply (zenon_L182_); trivial. % 10.36/10.55 apply (zenon_L183_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.36/10.55 apply (zenon_L817_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.36/10.55 apply (zenon_L35_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.36/10.55 apply (zenon_L595_); trivial. % 10.36/10.55 apply (zenon_L844_); trivial. % 10.36/10.55 (* end of lemma zenon_L851_ *) % 10.36/10.55 assert (zenon_L852_ : (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H31c zenon_H42 zenon_Hda zenon_H316 zenon_Hed zenon_H182 zenon_H51 zenon_H1ed zenon_H186. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H31c); [ zenon_intro zenon_H9a | zenon_intro zenon_H31d ]. % 10.36/10.55 apply (zenon_L836_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H31d); [ zenon_intro zenon_H8b | zenon_intro zenon_H31e ]. % 10.36/10.55 apply (zenon_L808_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_Hdb | zenon_intro zenon_H17a ]. % 10.36/10.55 apply (zenon_L307_); trivial. % 10.36/10.55 apply (zenon_L249_); trivial. % 10.36/10.55 (* end of lemma zenon_L852_ *) % 10.36/10.55 assert (zenon_L853_ : ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> False). % 10.36/10.55 do 0 intro. intros zenon_H202 zenon_H2e4 zenon_H284 zenon_H85 zenon_H18d zenon_H99 zenon_H293 zenon_H186 zenon_H182 zenon_H316 zenon_Hda zenon_H31c zenon_Hfd zenon_H287 zenon_H2a5 zenon_H28f zenon_H1ef zenon_Hce zenon_H2ef zenon_H1ed zenon_Hf4 zenon_H51 zenon_H42 zenon_H8c. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.55 apply (zenon_L1_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.55 apply (zenon_L2_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.55 apply (zenon_L3_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.55 apply (zenon_L4_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.55 apply (zenon_L5_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.55 apply (zenon_L6_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.55 apply (zenon_L744_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.55 apply (zenon_L799_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.55 apply (zenon_L10_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.55 apply (zenon_L750_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.55 apply (zenon_L13_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.55 apply (zenon_L801_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.55 apply (zenon_L15_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.55 apply (zenon_L802_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.55 apply (zenon_L803_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.55 apply (zenon_L19_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.55 apply (zenon_L20_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.55 apply (zenon_L21_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.55 apply (zenon_L757_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.55 apply (zenon_L839_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.55 apply (zenon_L24_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.55 apply (zenon_L25_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.55 apply (zenon_L26_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.55 apply (zenon_L27_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.55 apply (zenon_L805_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.55 apply (zenon_L31_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.55 apply (zenon_L32_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.55 apply (zenon_L806_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.55 apply (zenon_L852_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.55 apply (zenon_L56_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.55 apply (zenon_L784_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.55 apply (zenon_L147_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.55 apply (zenon_L148_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.55 apply (zenon_L785_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.55 apply (zenon_L150_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.55 apply (zenon_L672_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.55 apply (zenon_L786_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.55 apply (zenon_L154_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.55 apply (zenon_L155_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.55 apply (zenon_L288_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.55 apply (zenon_L157_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.55 apply (zenon_L158_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.55 apply (zenon_L159_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.55 apply (zenon_L160_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.55 apply (zenon_L679_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.55 apply (zenon_L265_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.55 apply (zenon_L164_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.55 apply (zenon_L165_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.55 apply (zenon_L166_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.55 apply (zenon_L810_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.55 apply (zenon_L811_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.55 apply (zenon_L169_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.55 apply (zenon_L812_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.55 apply (zenon_L172_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.55 apply (zenon_L484_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.55 apply (zenon_L174_); trivial. % 10.36/10.55 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.56 apply (zenon_L814_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.56 apply (zenon_L828_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.56 apply (zenon_L178_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.56 apply (zenon_L179_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.56 apply (zenon_L180_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.56 apply (zenon_L181_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.56 apply (zenon_L182_); trivial. % 10.36/10.56 apply (zenon_L183_); trivial. % 10.36/10.56 (* end of lemma zenon_L853_ *) % 10.36/10.56 assert (zenon_L854_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e0)) -> False). % 10.36/10.56 do 0 intro. intros zenon_H244 zenon_H130 zenon_H5a zenon_H154 zenon_H120 zenon_H8c zenon_H42 zenon_H51 zenon_Hf4 zenon_H2ef zenon_Hce zenon_H1ef zenon_H28f zenon_H2a5 zenon_H287 zenon_Hfd zenon_H31c zenon_Hda zenon_H316 zenon_H182 zenon_H186 zenon_H293 zenon_H99 zenon_H18d zenon_H85 zenon_H284 zenon_H2e4 zenon_H202 zenon_He9 zenon_H79. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.36/10.56 apply (zenon_L133_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.36/10.56 apply (zenon_L93_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.36/10.56 apply (zenon_L853_); trivial. % 10.36/10.56 apply (zenon_L548_); trivial. % 10.36/10.56 (* end of lemma zenon_L854_ *) % 10.36/10.56 assert (zenon_L855_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H15b zenon_Hc1 zenon_H79 zenon_H154 zenon_H5a zenon_H130 zenon_H2a8 zenon_Hd5 zenon_He9 zenon_H128 zenon_H78 zenon_H244 zenon_H202 zenon_H2e4 zenon_H284 zenon_H85 zenon_H18d zenon_H99 zenon_H293 zenon_H186 zenon_H182 zenon_H316 zenon_Hda zenon_H31c zenon_Hfd zenon_H287 zenon_H2a5 zenon_H28f zenon_H1ef zenon_Hce zenon_H2ef zenon_Hf4 zenon_H51 zenon_H42 zenon_H8c. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.36/10.56 apply (zenon_L658_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.36/10.56 apply (zenon_L854_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.36/10.56 apply (zenon_L60_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.36/10.56 apply (zenon_L616_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.36/10.56 exact (zenon_H78 zenon_H13b). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.36/10.56 apply (zenon_L77_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.36/10.56 apply (zenon_L249_); trivial. % 10.36/10.56 apply (zenon_L397_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.36/10.56 apply (zenon_L60_); trivial. % 10.36/10.56 apply (zenon_L853_); trivial. % 10.36/10.56 (* end of lemma zenon_L855_ *) % 10.36/10.56 assert (zenon_L856_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H12d zenon_H6b zenon_H1b2 zenon_H15b zenon_Hc1 zenon_H79 zenon_H154 zenon_H5a zenon_H130 zenon_H2a8 zenon_Hd5 zenon_He9 zenon_H78 zenon_H244 zenon_H202 zenon_H2e4 zenon_H284 zenon_H85 zenon_H18d zenon_H99 zenon_H293 zenon_H186 zenon_H182 zenon_H316 zenon_Hda zenon_H31c zenon_Hfd zenon_H287 zenon_H2a5 zenon_H28f zenon_H1ef zenon_Hce zenon_H2ef zenon_Hf4 zenon_H51 zenon_H42 zenon_H8c. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.56 apply (zenon_L494_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.56 exact (zenon_H6b zenon_H6f). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.56 apply (zenon_L259_); trivial. % 10.36/10.56 apply (zenon_L855_); trivial. % 10.36/10.56 (* end of lemma zenon_L856_ *) % 10.36/10.56 assert (zenon_L857_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.56 do 0 intro. intros zenon_H75 zenon_He9 zenon_H67. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H6a. zenon_intro zenon_H77. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H6b. zenon_intro zenon_H2a. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.36/10.56 apply (zenon_L548_); trivial. % 10.36/10.56 (* end of lemma zenon_L857_ *) % 10.36/10.56 assert (zenon_L858_ : (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (e3))) -> ((op (e3) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e3) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> (~((e0) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H244 zenon_H78 zenon_H252 zenon_Hfd zenon_H186 zenon_H51 zenon_H182 zenon_H187 zenon_Hda zenon_H42 zenon_H31c zenon_H75 zenon_He9. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.36/10.56 exact (zenon_H78 zenon_H13b). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.36/10.56 apply (zenon_L199_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.36/10.56 apply (zenon_L837_); trivial. % 10.36/10.56 apply (zenon_L857_); trivial. % 10.36/10.56 (* end of lemma zenon_L858_ *) % 10.36/10.56 assert (zenon_L859_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e0)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e0))\/(((op (e3) (e2)) = (e1))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e2)) = (e3))))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3)))))) -> (((op (e1) (e2)) = (e0))\/(((op (e1) (e2)) = (e1))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((op (e3) (e0)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H30e zenon_H47 zenon_H6a zenon_H104 zenon_H12d zenon_H6b zenon_H1b2 zenon_H15b zenon_H79 zenon_H154 zenon_H130 zenon_H2a8 zenon_Hd5 zenon_H8c zenon_H289 zenon_H293 zenon_H99 zenon_H2ef zenon_Hce zenon_H1ef zenon_H28f zenon_H2a5 zenon_H287 zenon_H316 zenon_H18d zenon_H284 zenon_H2e4 zenon_H202 zenon_H27c zenon_H318 zenon_Hf4 zenon_H2db zenon_H85 zenon_He9 zenon_H75 zenon_H31c zenon_H42 zenon_Hda zenon_H182 zenon_H186 zenon_Hfd zenon_H78 zenon_H244 zenon_H51 zenon_H278 zenon_H1ee. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H1f | zenon_intro zenon_H30f ]. % 10.36/10.56 apply (zenon_L11_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H95 | zenon_intro zenon_H310 ]. % 10.36/10.56 apply (zenon_L394_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H131 ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.56 apply (zenon_L856_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.56 apply (zenon_L248_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.56 apply (zenon_L658_); trivial. % 10.36/10.56 exact (zenon_H78 zenon_H13b). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.36/10.56 apply (zenon_L421_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.36/10.56 apply (zenon_L817_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.36/10.56 apply (zenon_L328_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H136 | zenon_intro zenon_H2dc ]. % 10.36/10.56 apply (zenon_L628_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H252 | zenon_intro zenon_H2dd ]. % 10.36/10.56 apply (zenon_L858_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H2d9 | zenon_intro zenon_Hd3 ]. % 10.36/10.56 apply (zenon_L754_); trivial. % 10.36/10.56 exact (zenon_H1ee zenon_Hd3). % 10.36/10.56 (* end of lemma zenon_L859_ *) % 10.36/10.56 assert (zenon_L860_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e0)) = (e1))\/(((op (e0) (e0)) = (e2))\/((op (e0) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H303 zenon_H37 zenon_H2d zenon_H2f zenon_Hc0 zenon_Hb9 zenon_H58. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H303); [ zenon_intro zenon_H1f | zenon_intro zenon_H304 ]. % 10.36/10.56 apply (zenon_L7_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H304); [ zenon_intro zenon_H31 | zenon_intro zenon_H305 ]. % 10.36/10.56 exact (zenon_H2f zenon_H31). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H305); [ zenon_intro zenon_H46 | zenon_intro zenon_H5a ]. % 10.36/10.56 apply (zenon_L88_); trivial. % 10.36/10.56 exact (zenon_H58 zenon_H5a). % 10.36/10.56 (* end of lemma zenon_L860_ *) % 10.36/10.56 assert (zenon_L861_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H17e zenon_H104 zenon_H6a zenon_Ha3 zenon_H150 zenon_Hda zenon_H67 zenon_H29d. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.56 apply (zenon_L248_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.56 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.56 apply (zenon_L308_); trivial. % 10.36/10.56 apply (zenon_L395_); trivial. % 10.36/10.56 (* end of lemma zenon_L861_ *) % 10.36/10.56 assert (zenon_L862_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H15e zenon_H58 zenon_He9 zenon_H2d zenon_H29d zenon_Hda zenon_Ha3 zenon_H6a zenon_H104 zenon_H17e zenon_H67 zenon_He6. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.56 exact (zenon_H58 zenon_H5a). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.56 apply (zenon_L134_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.56 apply (zenon_L861_); trivial. % 10.36/10.56 apply (zenon_L186_); trivial. % 10.36/10.56 (* end of lemma zenon_L862_ *) % 10.36/10.56 assert (zenon_L863_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H15e zenon_H58 zenon_He9 zenon_H2d zenon_Hfd zenon_Hcd zenon_H67 zenon_He6. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.56 exact (zenon_H58 zenon_H5a). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.56 apply (zenon_L134_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.56 apply (zenon_L91_); trivial. % 10.36/10.56 apply (zenon_L186_); trivial. % 10.36/10.56 (* end of lemma zenon_L863_ *) % 10.36/10.56 assert (zenon_L864_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H3c zenon_H191 zenon_H17e zenon_H104 zenon_Ha3 zenon_Hda zenon_H29d zenon_H287 zenon_H1a3 zenon_H85 zenon_He6 zenon_H67 zenon_Hfd zenon_He9 zenon_H58 zenon_H15e zenon_Hd4 zenon_H157. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H2d. zenon_intro zenon_H3d. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H2f. zenon_intro zenon_H80. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.56 exact (zenon_H2f zenon_H31). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.56 apply (zenon_L862_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.56 apply (zenon_L260_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.56 exact (zenon_H58 zenon_H5a). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.56 apply (zenon_L134_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.56 apply (zenon_L565_); trivial. % 10.36/10.56 apply (zenon_L186_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.56 apply (zenon_L486_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.56 apply (zenon_L863_); trivial. % 10.36/10.56 apply (zenon_L240_); trivial. % 10.36/10.56 (* end of lemma zenon_L864_ *) % 10.36/10.56 assert (zenon_L865_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.56 do 0 intro. intros zenon_H3e zenon_H104 zenon_H67. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H2d. zenon_intro zenon_H3f. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H2f. zenon_intro zenon_H83. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.36/10.56 apply (zenon_L286_); trivial. % 10.36/10.56 (* end of lemma zenon_L865_ *) % 10.36/10.56 assert (zenon_L866_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H15b zenon_Hfd zenon_Hb9 zenon_H119 zenon_H100 zenon_Hff zenon_H67 zenon_Hd5. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.36/10.56 apply (zenon_L92_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.36/10.56 apply (zenon_L212_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.36/10.56 exact (zenon_Hff zenon_Hfc). % 10.36/10.56 apply (zenon_L397_); trivial. % 10.36/10.56 (* end of lemma zenon_L866_ *) % 10.36/10.56 assert (zenon_L867_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H15e zenon_H58 zenon_Hd5 zenon_Hff zenon_H100 zenon_Hb9 zenon_Hfd zenon_H15b zenon_He9 zenon_H42 zenon_H67 zenon_He6. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.56 exact (zenon_H58 zenon_H5a). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.56 apply (zenon_L866_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.56 apply (zenon_L616_); trivial. % 10.36/10.56 apply (zenon_L186_); trivial. % 10.36/10.56 (* end of lemma zenon_L867_ *) % 10.36/10.56 assert (zenon_L868_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H15e zenon_H58 zenon_H31 zenon_H136 zenon_He9 zenon_H42 zenon_H67 zenon_He6. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.56 exact (zenon_H58 zenon_H5a). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.56 apply (zenon_L202_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.56 apply (zenon_L616_); trivial. % 10.36/10.56 apply (zenon_L186_); trivial. % 10.36/10.56 (* end of lemma zenon_L868_ *) % 10.36/10.56 assert (zenon_L869_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e2)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H281 zenon_H44 zenon_H177 zenon_H91 zenon_H15b zenon_Hfd zenon_H100 zenon_Hff zenon_Hd5 zenon_H15e zenon_H58 zenon_H31 zenon_He9 zenon_H42 zenon_H67 zenon_He6. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.56 exact (zenon_H44 zenon_H46). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.56 apply (zenon_L197_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.56 apply (zenon_L867_); trivial. % 10.36/10.56 apply (zenon_L868_); trivial. % 10.36/10.56 (* end of lemma zenon_L869_ *) % 10.36/10.56 assert (zenon_L870_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H15e zenon_H58 zenon_H104 zenon_Hf6 zenon_He9 zenon_H42 zenon_H67 zenon_He6. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.56 exact (zenon_H58 zenon_H5a). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.56 apply (zenon_L99_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.56 apply (zenon_L616_); trivial. % 10.36/10.56 apply (zenon_L186_); trivial. % 10.36/10.56 (* end of lemma zenon_L870_ *) % 10.36/10.56 assert (zenon_L871_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H17e zenon_H104 zenon_H6a zenon_Ha3 zenon_He9 zenon_H27c zenon_H42 zenon_H91 zenon_H136 zenon_H85 zenon_H245 zenon_H67 zenon_H29d. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.56 apply (zenon_L248_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.56 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.56 apply (zenon_L628_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.56 apply (zenon_L372_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.56 apply (zenon_L322_); trivial. % 10.36/10.56 apply (zenon_L548_); trivial. % 10.36/10.56 apply (zenon_L395_); trivial. % 10.36/10.56 (* end of lemma zenon_L871_ *) % 10.36/10.56 assert (zenon_L872_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1a2 zenon_H2f zenon_H99 zenon_H2d zenon_H103 zenon_Hce zenon_Hef zenon_H24b. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.56 exact (zenon_H2f zenon_H31). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.56 apply (zenon_L58_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.56 apply (zenon_L366_); trivial. % 10.36/10.56 apply (zenon_L191_); trivial. % 10.36/10.56 (* end of lemma zenon_L872_ *) % 10.36/10.56 assert (zenon_L873_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.36/10.56 do 0 intro. intros zenon_H5f zenon_Hef. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H56. zenon_intro zenon_H60. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H58. zenon_intro zenon_Hf2. % 10.36/10.56 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.36/10.56 exact (zenon_Hf3 zenon_Hef). % 10.36/10.56 (* end of lemma zenon_L873_ *) % 10.36/10.56 assert (zenon_L874_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> (~((op (e2) (e2)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H61 zenon_Hff. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H56. zenon_intro zenon_H62. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H58. zenon_intro zenon_H1d3. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.36/10.56 exact (zenon_Hff zenon_Hfc). % 10.36/10.56 (* end of lemma zenon_L874_ *) % 10.36/10.56 assert (zenon_L875_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H63. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H63). zenon_intro zenon_H56. zenon_intro zenon_H64. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H58. zenon_intro zenon_H65. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 10.36/10.56 exact (zenon_H66 zenon_H67). % 10.36/10.56 (* end of lemma zenon_L875_ *) % 10.36/10.56 assert (zenon_L876_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H70 zenon_Hef zenon_H138. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H6a. zenon_intro zenon_H72. % 10.36/10.56 apply (zenon_L84_); trivial. % 10.36/10.56 (* end of lemma zenon_L876_ *) % 10.36/10.56 assert (zenon_L877_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H89 zenon_Hef zenon_H316. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 10.36/10.56 apply (zenon_L807_); trivial. % 10.36/10.56 (* end of lemma zenon_L877_ *) % 10.36/10.56 assert (zenon_L878_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_Hed zenon_H58. % 10.36/10.56 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hef. zenon_intro zenon_Hee. % 10.36/10.56 apply (zenon_and_s _ _ zenon_Hee). zenon_intro zenon_Ha3. zenon_intro zenon_H57. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.36/10.56 exact (zenon_H58 zenon_H5a). % 10.36/10.56 (* end of lemma zenon_L878_ *) % 10.36/10.56 assert (zenon_L879_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> (~((op (e2) (e2)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H16f zenon_Hff. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hef. zenon_intro zenon_H170. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_Ha3. zenon_intro zenon_H1d3. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.36/10.56 exact (zenon_Hff zenon_Hfc). % 10.36/10.56 (* end of lemma zenon_L879_ *) % 10.36/10.56 assert (zenon_L880_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1a8. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1a8). zenon_intro zenon_Hef. zenon_intro zenon_H1a9. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_Ha3. zenon_intro zenon_H65. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 10.36/10.56 exact (zenon_H66 zenon_H67). % 10.36/10.56 (* end of lemma zenon_L880_ *) % 10.36/10.56 assert (zenon_L881_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H67 zenon_H127 zenon_H2ed. % 10.36/10.56 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ]. % 10.36/10.56 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 10.36/10.56 intro zenon_D_pnotp. % 10.36/10.56 apply zenon_H2ed. % 10.36/10.56 rewrite <- zenon_D_pnotp. % 10.36/10.56 exact zenon_Hd6. % 10.36/10.56 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.36/10.56 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2ee]. % 10.36/10.56 congruence. % 10.36/10.56 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 10.36/10.56 intro zenon_D_pnotp. % 10.36/10.56 apply zenon_H2ee. % 10.36/10.56 rewrite <- zenon_D_pnotp. % 10.36/10.56 exact zenon_H67. % 10.36/10.56 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2f1]. % 10.36/10.56 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 10.36/10.56 congruence. % 10.36/10.56 apply zenon_Hd7. apply refl_equal. % 10.36/10.56 apply zenon_H2f1. apply sym_equal. exact zenon_H127. % 10.36/10.56 apply zenon_Hd7. apply refl_equal. % 10.36/10.56 apply zenon_Hd7. apply refl_equal. % 10.36/10.56 (* end of lemma zenon_L881_ *) % 10.36/10.56 assert (zenon_L882_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H289 zenon_H58 zenon_H2ed zenon_H6f zenon_H14b zenon_Hf6 zenon_H262 zenon_H2f2 zenon_Hfd zenon_Hb9 zenon_H67 zenon_H26e. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.56 exact (zenon_H58 zenon_H5a). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2f2); [ zenon_intro zenon_H128 | zenon_intro zenon_H2f3 ]. % 10.36/10.56 apply (zenon_L767_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2f3); [ zenon_intro zenon_H175 | zenon_intro zenon_H2f4 ]. % 10.36/10.56 apply (zenon_L124_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H252 | zenon_intro zenon_H127 ]. % 10.36/10.56 apply (zenon_L790_); trivial. % 10.36/10.56 apply (zenon_L881_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.56 apply (zenon_L92_); trivial. % 10.36/10.56 apply (zenon_L221_); trivial. % 10.36/10.56 (* end of lemma zenon_L882_ *) % 10.36/10.56 assert (zenon_L883_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H290 zenon_H71 zenon_H16e zenon_Hce zenon_Hb9 zenon_H287 zenon_Hff. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H74 | zenon_intro zenon_H291 ]. % 10.36/10.56 exact (zenon_H71 zenon_H74). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H103 | zenon_intro zenon_H292 ]. % 10.36/10.56 apply (zenon_L366_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfc ]. % 10.36/10.56 apply (zenon_L299_); trivial. % 10.36/10.56 exact (zenon_Hff zenon_Hfc). % 10.36/10.56 (* end of lemma zenon_L883_ *) % 10.36/10.56 assert (zenon_L884_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> ((op (e1) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.36/10.56 do 0 intro. intros zenon_Hca zenon_Hb9 zenon_H85 zenon_H6f zenon_H171 zenon_H71 zenon_H157 zenon_H56. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.36/10.56 apply (zenon_L417_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.36/10.56 apply (zenon_L762_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.36/10.56 exact (zenon_H71 zenon_H74). % 10.36/10.56 apply (zenon_L209_); trivial. % 10.36/10.56 (* end of lemma zenon_L884_ *) % 10.36/10.56 assert (zenon_L885_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3)))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1be zenon_H104 zenon_H67. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_Hc3. zenon_intro zenon_H1bf. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H163. zenon_intro zenon_H83. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.36/10.56 apply (zenon_L286_); trivial. % 10.36/10.56 (* end of lemma zenon_L885_ *) % 10.36/10.56 assert (zenon_L886_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> (~((op (e0) (e0)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1c9 zenon_H58. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_Hd4. zenon_intro zenon_H1ca. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1ca). zenon_intro zenon_Hff. zenon_intro zenon_H57. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.36/10.56 exact (zenon_H58 zenon_H5a). % 10.36/10.56 (* end of lemma zenon_L886_ *) % 10.36/10.56 assert (zenon_L887_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> ((op (e1) (e3)) = (e1)) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1cf zenon_Hef. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_Hd4. zenon_intro zenon_H1d0. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_Hff. zenon_intro zenon_Hf2. % 10.36/10.56 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.36/10.56 exact (zenon_Hf3 zenon_Hef). % 10.36/10.56 (* end of lemma zenon_L887_ *) % 10.36/10.56 assert (zenon_L888_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1d4. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_Hd4. zenon_intro zenon_H1d5. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_Hff. zenon_intro zenon_H65. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 10.36/10.56 exact (zenon_H66 zenon_H67). % 10.36/10.56 (* end of lemma zenon_L888_ *) % 10.36/10.56 assert (zenon_L889_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1d8 zenon_H67 zenon_H26e. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1d8). zenon_intro zenon_H13b. zenon_intro zenon_H1d9. % 10.36/10.56 apply (zenon_L221_); trivial. % 10.36/10.56 (* end of lemma zenon_L889_ *) % 10.36/10.56 assert (zenon_L890_ : (((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1da zenon_H67 zenon_H26e. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_H13b. zenon_intro zenon_H1db. % 10.36/10.56 apply (zenon_L221_); trivial. % 10.36/10.56 (* end of lemma zenon_L890_ *) % 10.36/10.56 assert (zenon_L891_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1e1 zenon_H67 zenon_H2ed. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H127. zenon_intro zenon_H1e2. % 10.36/10.56 apply (zenon_L881_); trivial. % 10.36/10.56 (* end of lemma zenon_L891_ *) % 10.36/10.56 assert (zenon_L892_ : (((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1e6 zenon_H67 zenon_H2ed. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H127. zenon_intro zenon_H1e7. % 10.36/10.56 apply (zenon_L881_); trivial. % 10.36/10.56 (* end of lemma zenon_L892_ *) % 10.36/10.56 assert (zenon_L893_ : (((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1fa. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1fa). zenon_intro zenon_H67. zenon_intro zenon_H1fb. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H66. zenon_intro zenon_H57. % 10.36/10.56 exact (zenon_H66 zenon_H67). % 10.36/10.56 (* end of lemma zenon_L893_ *) % 10.36/10.56 assert (zenon_L894_ : (((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1fc. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1fc). zenon_intro zenon_H67. zenon_intro zenon_H1fd. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H66. zenon_intro zenon_Hf2. % 10.36/10.56 exact (zenon_H66 zenon_H67). % 10.36/10.56 (* end of lemma zenon_L894_ *) % 10.36/10.56 assert (zenon_L895_ : (((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1fe. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1fe). zenon_intro zenon_H67. zenon_intro zenon_H1ff. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1ff). zenon_intro zenon_H66. zenon_intro zenon_H1d3. % 10.36/10.56 exact (zenon_H66 zenon_H67). % 10.36/10.56 (* end of lemma zenon_L895_ *) % 10.36/10.56 assert (zenon_L896_ : (((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H200. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H200). zenon_intro zenon_H67. zenon_intro zenon_H201. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H201). zenon_intro zenon_H66. zenon_intro zenon_H65. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 10.36/10.56 exact (zenon_H66 zenon_H67). % 10.36/10.56 (* end of lemma zenon_L896_ *) % 10.36/10.56 assert (zenon_L897_ : (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H269 zenon_Hc7 zenon_H24b zenon_Hef zenon_H157 zenon_Hd4 zenon_H67 zenon_He6. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H269); [ zenon_intro zenon_H56 | zenon_intro zenon_H26a ]. % 10.36/10.56 apply (zenon_L209_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H198 | zenon_intro zenon_H26b ]. % 10.36/10.56 apply (zenon_L191_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_He5 | zenon_intro zenon_H158 ]. % 10.36/10.56 apply (zenon_L240_); trivial. % 10.36/10.56 apply (zenon_L186_); trivial. % 10.36/10.56 (* end of lemma zenon_L897_ *) % 10.36/10.56 assert (zenon_L898_ : (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.56 do 0 intro. intros zenon_H272 zenon_H2e7 zenon_H2d zenon_H99 zenon_He6 zenon_Hd4 zenon_H157 zenon_Hef zenon_H24b zenon_H269 zenon_He9 zenon_H67. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.36/10.56 apply (zenon_L496_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.36/10.56 apply (zenon_L71_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.36/10.56 apply (zenon_L897_); trivial. % 10.36/10.56 apply (zenon_L548_); trivial. % 10.36/10.56 (* end of lemma zenon_L898_ *) % 10.36/10.56 assert (zenon_L899_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.56 do 0 intro. intros zenon_H4b zenon_H272 zenon_H284 zenon_H99 zenon_He6 zenon_Hd4 zenon_H157 zenon_Hef zenon_H24b zenon_H269 zenon_He9 zenon_H67. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H42. zenon_intro zenon_H4c. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H272); [ zenon_intro zenon_H56 | zenon_intro zenon_H273 ]. % 10.36/10.56 apply (zenon_L619_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H274 ]. % 10.36/10.56 apply (zenon_L71_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H79 ]. % 10.36/10.56 apply (zenon_L897_); trivial. % 10.36/10.56 apply (zenon_L548_); trivial. % 10.36/10.56 (* end of lemma zenon_L899_ *) % 10.36/10.56 assert (zenon_L900_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> ((op (e2) (e3)) = (e2)) -> False). % 10.36/10.56 do 0 intro. intros zenon_H61 zenon_Hd4. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H56. zenon_intro zenon_H62. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H58. zenon_intro zenon_H1d3. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.36/10.56 exact (zenon_H122 zenon_Hd4). % 10.36/10.56 (* end of lemma zenon_L900_ *) % 10.36/10.56 assert (zenon_L901_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2)))))) -> ((op (e2) (e3)) = (e2)) -> False). % 10.36/10.56 do 0 intro. intros zenon_H16f zenon_Hd4. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hef. zenon_intro zenon_H170. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_Ha3. zenon_intro zenon_H1d3. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.36/10.56 exact (zenon_H122 zenon_Hd4). % 10.36/10.56 (* end of lemma zenon_L901_ *) % 10.36/10.56 assert (zenon_L902_ : (((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1)))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1ac zenon_Hd4 zenon_H1cb. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_Hb9. zenon_intro zenon_H1ad. % 10.36/10.56 apply (zenon_L162_); trivial. % 10.36/10.56 (* end of lemma zenon_L902_ *) % 10.36/10.56 assert (zenon_L903_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H1b7 zenon_Hd4 zenon_H2ea. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.36/10.56 apply (zenon_L515_); trivial. % 10.36/10.56 (* end of lemma zenon_L903_ *) % 10.36/10.56 assert (zenon_L904_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H320 zenon_H2e7 zenon_H269 zenon_H272 zenon_H284 zenon_H1cb zenon_H2ea zenon_H99 zenon_Hce zenon_H24b zenon_Hef zenon_H1a2 zenon_H67 zenon_H104 zenon_H281 zenon_H58 zenon_H15b zenon_Hd5 zenon_H100 zenon_Hfd zenon_He9 zenon_He6 zenon_H15e zenon_H177 zenon_H138 zenon_H316 zenon_H287 zenon_H290 zenon_H2f2 zenon_H2ed zenon_H14b zenon_H262 zenon_H289 zenon_H130 zenon_H135 zenon_H26e zenon_H145 zenon_H173 zenon_Hca zenon_H157 zenon_H171 zenon_H85 zenon_H308 zenon_Hc0 zenon_Hf4 zenon_Hc6 zenon_H124 zenon_H2cd zenon_H202. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_Hff | zenon_intro zenon_Hd4 ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.56 apply (zenon_L1_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.56 apply (zenon_L2_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.56 apply (zenon_L3_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.56 apply (zenon_L4_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.56 apply (zenon_L5_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.56 apply (zenon_L6_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H2d. zenon_intro zenon_H3d. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H2f. zenon_intro zenon_H80. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.36/10.56 apply (zenon_L872_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.56 apply (zenon_L865_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.56 apply (zenon_L10_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H42. zenon_intro zenon_H4c. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H44. zenon_intro zenon_H8f. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.56 apply (zenon_L869_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.56 apply (zenon_L870_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.56 apply (zenon_L421_); trivial. % 10.36/10.56 apply (zenon_L191_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.56 apply (zenon_L13_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.56 apply (zenon_L607_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.56 apply (zenon_L15_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.56 apply (zenon_L873_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.56 apply (zenon_L874_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.56 apply (zenon_L875_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.56 apply (zenon_L20_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.56 apply (zenon_L21_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.56 apply (zenon_L876_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.56 apply (zenon_L857_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.56 apply (zenon_L24_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.56 apply (zenon_L25_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.56 apply (zenon_L26_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.56 apply (zenon_L27_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.56 apply (zenon_L877_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.56 apply (zenon_L31_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.56 apply (zenon_L32_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.56 apply (zenon_L357_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.56 apply (zenon_L878_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.56 apply (zenon_L56_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.56 apply (zenon_L879_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.56 apply (zenon_L880_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.56 apply (zenon_L148_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_Hb9. zenon_intro zenon_H1ad. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H71. zenon_intro zenon_H24. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.56 apply (zenon_L350_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.56 apply (zenon_L882_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.56 apply (zenon_L883_); trivial. % 10.36/10.56 apply (zenon_L191_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.56 apply (zenon_L504_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.56 apply (zenon_L867_); trivial. % 10.36/10.56 apply (zenon_L884_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.56 apply (zenon_L150_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.56 apply (zenon_L692_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.56 apply (zenon_L227_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.56 apply (zenon_L154_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.56 apply (zenon_L155_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.56 apply (zenon_L885_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.56 apply (zenon_L157_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.56 apply (zenon_L158_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.56 apply (zenon_L159_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.56 apply (zenon_L160_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.56 apply (zenon_L886_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.56 apply (zenon_L887_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.56 apply (zenon_L164_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.56 apply (zenon_L888_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.56 apply (zenon_L166_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.56 apply (zenon_L889_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.56 apply (zenon_L890_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.56 apply (zenon_L169_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.56 apply (zenon_L891_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.56 apply (zenon_L172_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.56 apply (zenon_L892_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.56 apply (zenon_L174_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.56 apply (zenon_L523_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.56 apply (zenon_L388_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.56 apply (zenon_L178_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.56 apply (zenon_L179_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.56 apply (zenon_L893_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.56 apply (zenon_L894_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.56 apply (zenon_L895_); trivial. % 10.36/10.56 apply (zenon_L896_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.56 apply (zenon_L1_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.56 apply (zenon_L2_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.56 apply (zenon_L3_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.56 apply (zenon_L4_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.56 apply (zenon_L5_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.56 apply (zenon_L6_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H2d. zenon_intro zenon_H3d. % 10.36/10.56 apply (zenon_L898_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.56 apply (zenon_L865_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.56 apply (zenon_L10_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.56 apply (zenon_L899_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.56 apply (zenon_L13_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.56 apply (zenon_L607_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.56 apply (zenon_L15_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.56 apply (zenon_L873_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.56 apply (zenon_L900_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.56 apply (zenon_L875_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.56 apply (zenon_L20_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.56 apply (zenon_L21_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.56 apply (zenon_L876_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.56 apply (zenon_L857_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.56 apply (zenon_L24_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.56 apply (zenon_L25_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.56 apply (zenon_L26_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.56 apply (zenon_L27_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.56 apply (zenon_L877_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.56 apply (zenon_L31_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.56 apply (zenon_L32_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.56 apply (zenon_L357_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.56 apply (zenon_L878_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.56 apply (zenon_L56_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.56 apply (zenon_L901_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.56 apply (zenon_L880_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.56 apply (zenon_L148_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.56 apply (zenon_L902_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.56 apply (zenon_L150_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.56 apply (zenon_L692_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.56 apply (zenon_L903_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.56 apply (zenon_L154_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.56 apply (zenon_L155_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.56 apply (zenon_L885_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.56 apply (zenon_L157_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.56 apply (zenon_L158_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.56 apply (zenon_L159_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.56 apply (zenon_L160_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.56 apply (zenon_L886_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.56 apply (zenon_L887_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.56 apply (zenon_L164_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.56 apply (zenon_L888_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.56 apply (zenon_L166_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.56 apply (zenon_L889_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.56 apply (zenon_L890_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.56 apply (zenon_L169_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.56 apply (zenon_L891_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.56 apply (zenon_L172_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.56 apply (zenon_L892_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.56 apply (zenon_L174_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.56 apply (zenon_L523_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.56 apply (zenon_L388_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.56 apply (zenon_L178_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.56 apply (zenon_L179_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.56 apply (zenon_L893_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.56 apply (zenon_L894_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.56 apply (zenon_L895_); trivial. % 10.36/10.56 apply (zenon_L896_); trivial. % 10.36/10.56 (* end of lemma zenon_L904_ *) % 10.36/10.56 assert (zenon_L905_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H2ab zenon_H29d zenon_H245 zenon_H136 zenon_H42 zenon_H27c zenon_Ha3 zenon_H17e zenon_H91 zenon_H90 zenon_H320 zenon_H2e7 zenon_H269 zenon_H272 zenon_H284 zenon_H1cb zenon_H2ea zenon_H99 zenon_Hce zenon_H24b zenon_H1a2 zenon_H67 zenon_H104 zenon_H281 zenon_H58 zenon_H15b zenon_Hd5 zenon_H100 zenon_Hfd zenon_He9 zenon_He6 zenon_H15e zenon_H177 zenon_H138 zenon_H316 zenon_H287 zenon_H290 zenon_H2f2 zenon_H2ed zenon_H14b zenon_H262 zenon_H289 zenon_H130 zenon_H135 zenon_H26e zenon_H145 zenon_H173 zenon_Hca zenon_H157 zenon_H171 zenon_H85 zenon_H308 zenon_Hc0 zenon_Hf4 zenon_Hc6 zenon_H124 zenon_H2cd zenon_H202. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.36/10.56 apply (zenon_L871_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.36/10.56 apply (zenon_L310_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.36/10.56 exact (zenon_H90 zenon_H8b). % 10.36/10.56 apply (zenon_L904_); trivial. % 10.36/10.56 (* end of lemma zenon_L905_ *) % 10.36/10.56 assert (zenon_L906_ : (~((op (e0) (e0)) = (e2))) -> ((op (e2) (e0)) = (e1)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e0) (e3)) = (e1))\/(((op (e0) (e3)) = (e2))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e1)) = (e0))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e1)) = (e2))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H44 zenon_Hfa zenon_H2ab zenon_H29d zenon_H245 zenon_H42 zenon_H27c zenon_Ha3 zenon_H17e zenon_H91 zenon_H90 zenon_H320 zenon_H2e7 zenon_H269 zenon_H272 zenon_H284 zenon_H1cb zenon_H2ea zenon_H99 zenon_Hce zenon_H24b zenon_H1a2 zenon_H67 zenon_H104 zenon_H281 zenon_H58 zenon_H15b zenon_Hd5 zenon_H100 zenon_Hfd zenon_He9 zenon_He6 zenon_H15e zenon_H177 zenon_H138 zenon_H316 zenon_H287 zenon_H290 zenon_H2f2 zenon_H2ed zenon_H14b zenon_H262 zenon_H289 zenon_H130 zenon_H135 zenon_H26e zenon_H145 zenon_H173 zenon_Hca zenon_H157 zenon_H171 zenon_H85 zenon_H308 zenon_Hc0 zenon_Hf4 zenon_Hc6 zenon_H124 zenon_H2cd zenon_H202. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.56 exact (zenon_H44 zenon_H46). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.56 apply (zenon_L197_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.56 apply (zenon_L59_); trivial. % 10.36/10.56 apply (zenon_L905_); trivial. % 10.36/10.56 (* end of lemma zenon_L906_ *) % 10.36/10.56 assert (zenon_L907_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (e1))) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H2ab zenon_H29d zenon_H67 zenon_H245 zenon_H99 zenon_H133 zenon_H42 zenon_H27c zenon_He9 zenon_Ha3 zenon_H104 zenon_H17e zenon_H91 zenon_Hf4 zenon_H90 zenon_H198 zenon_H24b. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.56 apply (zenon_L248_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.56 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.56 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.56 apply (zenon_L110_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.56 apply (zenon_L372_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.56 apply (zenon_L322_); trivial. % 10.36/10.56 apply (zenon_L548_); trivial. % 10.36/10.56 apply (zenon_L395_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.36/10.56 apply (zenon_L310_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.36/10.56 exact (zenon_H90 zenon_H8b). % 10.36/10.56 apply (zenon_L191_); trivial. % 10.36/10.56 (* end of lemma zenon_L907_ *) % 10.36/10.56 assert (zenon_L908_ : (((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_H5f zenon_Ha3. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H56. zenon_intro zenon_H60. % 10.36/10.56 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H58. zenon_intro zenon_Hf2. % 10.36/10.56 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.36/10.56 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.56 (* end of lemma zenon_L908_ *) % 10.36/10.56 assert (zenon_L909_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e2)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_Hb3 zenon_H6b zenon_H6a zenon_H177 zenon_H17a zenon_H128 zenon_Ha3. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.36/10.56 exact (zenon_H6b zenon_H6f). % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.36/10.56 apply (zenon_L282_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.36/10.56 apply (zenon_L372_); trivial. % 10.36/10.56 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.56 (* end of lemma zenon_L909_ *) % 10.36/10.56 assert (zenon_L910_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.36/10.56 do 0 intro. intros zenon_Hb3 zenon_H6b zenon_H6a zenon_H177 zenon_H171 zenon_Hc3 zenon_Ha3. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.36/10.56 exact (zenon_H6b zenon_H6f). % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.36/10.56 apply (zenon_L282_); trivial. % 10.36/10.56 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.36/10.56 apply (zenon_L477_); trivial. % 10.36/10.56 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.57 (* end of lemma zenon_L910_ *) % 10.36/10.57 assert (zenon_L911_ : (((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2)))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H3c zenon_H56 zenon_H2e7. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H2d. zenon_intro zenon_H3d. % 10.36/10.57 apply (zenon_L496_); trivial. % 10.36/10.57 (* end of lemma zenon_L911_ *) % 10.36/10.57 assert (zenon_L912_ : (((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1)))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H4b zenon_H56 zenon_H284. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H42. zenon_intro zenon_H4c. % 10.36/10.57 apply (zenon_L619_); trivial. % 10.36/10.57 (* end of lemma zenon_L912_ *) % 10.36/10.57 assert (zenon_L913_ : (((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.36/10.57 do 0 intro. intros zenon_Hed zenon_H56. % 10.36/10.57 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hef. zenon_intro zenon_Hee. % 10.36/10.57 apply (zenon_and_s _ _ zenon_Hee). zenon_intro zenon_Ha3. zenon_intro zenon_H57. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.36/10.57 exact (zenon_H59 zenon_H56). % 10.36/10.57 (* end of lemma zenon_L913_ *) % 10.36/10.57 assert (zenon_L914_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.57 do 0 intro. intros zenon_H2c5 zenon_H85 zenon_H56 zenon_Hf4 zenon_Hef zenon_H1cb zenon_Hb9 zenon_Hfd zenon_H67. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.36/10.57 apply (zenon_L663_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.36/10.57 apply (zenon_L97_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.36/10.57 apply (zenon_L162_); trivial. % 10.36/10.57 apply (zenon_L353_); trivial. % 10.36/10.57 (* end of lemma zenon_L914_ *) % 10.36/10.57 assert (zenon_L915_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.57 do 0 intro. intros zenon_H2c5 zenon_H85 zenon_H56 zenon_Hf4 zenon_Hef zenon_H2ea zenon_Hc3 zenon_Hfd zenon_H67. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.36/10.57 apply (zenon_L663_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.36/10.57 apply (zenon_L97_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.36/10.57 apply (zenon_L515_); trivial. % 10.36/10.57 apply (zenon_L353_); trivial. % 10.36/10.57 (* end of lemma zenon_L915_ *) % 10.36/10.57 assert (zenon_L916_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0)))))) -> ((op (e0) (e3)) = (e0)) -> False). % 10.36/10.57 do 0 intro. intros zenon_H1c9 zenon_H56. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_Hd4. zenon_intro zenon_H1ca. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1ca). zenon_intro zenon_Hff. zenon_intro zenon_H57. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.36/10.57 exact (zenon_H59 zenon_H56). % 10.36/10.57 (* end of lemma zenon_L916_ *) % 10.36/10.57 assert (zenon_L917_ : ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.57 do 0 intro. intros zenon_H202 zenon_H2e7 zenon_H284 zenon_H138 zenon_H316 zenon_Hff zenon_H1cb zenon_He9 zenon_Hfd zenon_H2ea zenon_Hf4 zenon_H85 zenon_H2c5 zenon_H104 zenon_H56 zenon_Hef zenon_H26e zenon_H2ed zenon_H2cd zenon_H67. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.57 apply (zenon_L1_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.57 apply (zenon_L2_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.57 apply (zenon_L3_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.57 apply (zenon_L4_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.57 apply (zenon_L5_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.57 apply (zenon_L6_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.57 apply (zenon_L911_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.57 apply (zenon_L865_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.57 apply (zenon_L10_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.57 apply (zenon_L912_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.57 apply (zenon_L13_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.57 apply (zenon_L607_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.57 apply (zenon_L15_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.57 apply (zenon_L873_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.57 apply (zenon_L874_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.57 apply (zenon_L875_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.57 apply (zenon_L20_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.57 apply (zenon_L21_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.57 apply (zenon_L876_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.57 apply (zenon_L857_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.57 apply (zenon_L24_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.57 apply (zenon_L25_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.57 apply (zenon_L26_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.57 apply (zenon_L27_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.57 apply (zenon_L877_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.57 apply (zenon_L31_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.57 apply (zenon_L32_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.57 apply (zenon_L357_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.57 apply (zenon_L913_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.57 apply (zenon_L56_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.57 apply (zenon_L879_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.57 apply (zenon_L880_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.57 apply (zenon_L148_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_Hb9. zenon_intro zenon_H1ad. % 10.36/10.57 apply (zenon_L914_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.57 apply (zenon_L150_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.57 apply (zenon_L692_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.36/10.57 apply (zenon_L915_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.57 apply (zenon_L154_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.57 apply (zenon_L155_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.57 apply (zenon_L885_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.57 apply (zenon_L157_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.57 apply (zenon_L158_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.57 apply (zenon_L159_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.57 apply (zenon_L160_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.57 apply (zenon_L916_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.57 apply (zenon_L887_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.57 apply (zenon_L164_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.57 apply (zenon_L888_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.57 apply (zenon_L166_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.57 apply (zenon_L889_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.57 apply (zenon_L890_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.57 apply (zenon_L169_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.57 apply (zenon_L891_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.57 apply (zenon_L172_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.57 apply (zenon_L892_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.57 apply (zenon_L174_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.57 apply (zenon_L523_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.57 apply (zenon_L388_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.57 apply (zenon_L178_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.57 apply (zenon_L179_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.57 apply (zenon_L893_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.57 apply (zenon_L894_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.57 apply (zenon_L895_); trivial. % 10.36/10.57 apply (zenon_L896_); trivial. % 10.36/10.57 (* end of lemma zenon_L917_ *) % 10.36/10.57 assert (zenon_L918_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H320 zenon_H56 zenon_H2e7 zenon_H67 zenon_H104 zenon_H284 zenon_Hfd zenon_Hef zenon_H138 zenon_He9 zenon_H316 zenon_H85 zenon_Hf4 zenon_H1cb zenon_H2c5 zenon_H2ea zenon_H26e zenon_H2ed zenon_H2cd zenon_H202. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_Hff | zenon_intro zenon_Hd4 ]. % 10.36/10.57 apply (zenon_L917_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.57 apply (zenon_L1_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.57 apply (zenon_L2_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.57 apply (zenon_L3_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.57 apply (zenon_L4_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.57 apply (zenon_L5_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.57 apply (zenon_L6_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.57 apply (zenon_L911_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.57 apply (zenon_L865_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.57 apply (zenon_L10_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.57 apply (zenon_L912_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.57 apply (zenon_L13_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.57 apply (zenon_L607_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.57 apply (zenon_L15_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.57 apply (zenon_L873_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.57 apply (zenon_L900_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.57 apply (zenon_L875_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.57 apply (zenon_L20_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.57 apply (zenon_L21_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.57 apply (zenon_L876_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.57 apply (zenon_L857_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.57 apply (zenon_L24_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.57 apply (zenon_L25_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.57 apply (zenon_L26_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.57 apply (zenon_L27_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.57 apply (zenon_L877_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.57 apply (zenon_L31_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.57 apply (zenon_L32_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.57 apply (zenon_L357_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.57 apply (zenon_L913_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.57 apply (zenon_L56_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.57 apply (zenon_L901_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.57 apply (zenon_L880_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.57 apply (zenon_L148_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.57 apply (zenon_L902_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.57 apply (zenon_L150_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.57 apply (zenon_L692_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.57 apply (zenon_L903_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.57 apply (zenon_L154_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.57 apply (zenon_L155_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.57 apply (zenon_L885_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.57 apply (zenon_L157_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.57 apply (zenon_L158_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.57 apply (zenon_L159_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.57 apply (zenon_L160_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.57 apply (zenon_L916_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.57 apply (zenon_L887_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.57 apply (zenon_L164_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.57 apply (zenon_L888_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.57 apply (zenon_L166_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.57 apply (zenon_L889_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.57 apply (zenon_L890_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.57 apply (zenon_L169_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.57 apply (zenon_L891_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.57 apply (zenon_L172_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.57 apply (zenon_L892_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.57 apply (zenon_L174_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.57 apply (zenon_L523_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.57 apply (zenon_L388_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.57 apply (zenon_L178_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.57 apply (zenon_L179_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.57 apply (zenon_L893_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.57 apply (zenon_L894_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.57 apply (zenon_L895_); trivial. % 10.36/10.57 apply (zenon_L896_); trivial. % 10.36/10.57 (* end of lemma zenon_L918_ *) % 10.36/10.57 assert (zenon_L919_ : (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e1)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H266 zenon_H56 zenon_H24b zenon_H107 zenon_Hc6 zenon_Hd4 zenon_H67 zenon_H29d. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H266); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H267 ]. % 10.36/10.57 apply (zenon_L270_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H267); [ zenon_intro zenon_Hef | zenon_intro zenon_H268 ]. % 10.36/10.57 apply (zenon_L75_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H268); [ zenon_intro zenon_Hdd | zenon_intro zenon_H17c ]. % 10.36/10.57 apply (zenon_L238_); trivial. % 10.36/10.57 apply (zenon_L395_); trivial. % 10.36/10.57 (* end of lemma zenon_L919_ *) % 10.36/10.57 assert (zenon_L920_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.57 do 0 intro. intros zenon_H298 zenon_H99 zenon_H202 zenon_H2cd zenon_H2ed zenon_H26e zenon_H2ea zenon_H2c5 zenon_H1cb zenon_Hf4 zenon_H85 zenon_H316 zenon_He9 zenon_H138 zenon_Hfd zenon_H284 zenon_H2e7 zenon_H320 zenon_H29d zenon_Hd4 zenon_Hc6 zenon_H24b zenon_H56 zenon_H266 zenon_H104 zenon_H67. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H198 | zenon_intro zenon_H299 ]. % 10.36/10.57 apply (zenon_L670_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_Hef | zenon_intro zenon_H29a ]. % 10.36/10.57 apply (zenon_L918_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H107 | zenon_intro zenon_H189 ]. % 10.36/10.57 apply (zenon_L919_); trivial. % 10.36/10.57 apply (zenon_L286_); trivial. % 10.36/10.57 (* end of lemma zenon_L920_ *) % 10.36/10.57 assert (zenon_L921_ : (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.57 do 0 intro. intros zenon_He0 zenon_H73 zenon_Ha3 zenon_H171 zenon_H177 zenon_H6a zenon_H6b zenon_Hb3 zenon_H74 zenon_H298 zenon_H99 zenon_H202 zenon_H2cd zenon_H2ed zenon_H26e zenon_H2ea zenon_H2c5 zenon_H1cb zenon_Hf4 zenon_H85 zenon_H316 zenon_He9 zenon_H138 zenon_Hfd zenon_H284 zenon_H2e7 zenon_H320 zenon_H29d zenon_Hc6 zenon_H24b zenon_H56 zenon_H266 zenon_H104 zenon_H67. % 10.36/10.57 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.36/10.57 exact (zenon_H73 zenon_Hb9). % 10.36/10.57 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.36/10.57 apply (zenon_L910_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.36/10.57 apply (zenon_L595_); trivial. % 10.36/10.57 apply (zenon_L920_); trivial. % 10.36/10.57 (* end of lemma zenon_L921_ *) % 10.36/10.57 assert (zenon_L922_ : (((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2)))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.57 do 0 intro. intros zenon_H70 zenon_H308 zenon_H245 zenon_H130 zenon_H278 zenon_He6 zenon_H17e zenon_Hda zenon_H58 zenon_H15e zenon_Hce zenon_He0 zenon_Ha3 zenon_H171 zenon_H177 zenon_Hb3 zenon_H298 zenon_H99 zenon_H202 zenon_H2cd zenon_H2ed zenon_H26e zenon_H2ea zenon_H2c5 zenon_H1cb zenon_Hf4 zenon_H85 zenon_H316 zenon_He9 zenon_H138 zenon_Hfd zenon_H284 zenon_H2e7 zenon_H320 zenon_H29d zenon_Hc6 zenon_H24b zenon_H266 zenon_H104 zenon_H67. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H6a. zenon_intro zenon_H72. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H6b. zenon_intro zenon_H27. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.57 apply (zenon_L248_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.57 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.57 apply (zenon_L81_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.57 apply (zenon_L909_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.57 apply (zenon_L298_); trivial. % 10.36/10.57 apply (zenon_L548_); trivial. % 10.36/10.57 apply (zenon_L395_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.57 apply (zenon_L862_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.57 apply (zenon_L677_); trivial. % 10.36/10.57 apply (zenon_L921_); trivial. % 10.36/10.57 (* end of lemma zenon_L922_ *) % 10.36/10.57 assert (zenon_L923_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e1) (e0)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.36/10.57 do 0 intro. intros zenon_Hb3 zenon_H13c zenon_H252 zenon_H9c zenon_H8b zenon_H8c zenon_Ha3. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.36/10.57 apply (zenon_L790_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.36/10.57 apply (zenon_L36_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.36/10.57 exact (zenon_H8c zenon_H91). % 10.36/10.57 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.57 (* end of lemma zenon_L923_ *) % 10.36/10.57 assert (zenon_L924_ : (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> False). % 10.36/10.57 do 0 intro. intros zenon_H2bc zenon_H45 zenon_Hda zenon_H8b zenon_H2d9 zenon_H27c zenon_H133 zenon_H46. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H42 | zenon_intro zenon_H2bd ]. % 10.36/10.57 exact (zenon_H45 zenon_H42). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2bd); [ zenon_intro zenon_H16e | zenon_intro zenon_H2be ]. % 10.36/10.57 apply (zenon_L131_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2be); [ zenon_intro zenon_Hcd | zenon_intro zenon_H150 ]. % 10.36/10.57 apply (zenon_L401_); trivial. % 10.36/10.57 apply (zenon_L565_); trivial. % 10.36/10.57 (* end of lemma zenon_L924_ *) % 10.36/10.57 assert (zenon_L925_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.36/10.57 do 0 intro. intros zenon_Hb3 zenon_H173 zenon_H2d zenon_H9c zenon_H8b zenon_H8c zenon_Ha3. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb3); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb4 ]. % 10.36/10.57 apply (zenon_L504_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H36 | zenon_intro zenon_Hb5 ]. % 10.36/10.57 apply (zenon_L36_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H91 | zenon_intro zenon_Ha2 ]. % 10.36/10.57 exact (zenon_H8c zenon_H91). % 10.36/10.57 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.57 (* end of lemma zenon_L925_ *) % 10.36/10.57 assert (zenon_L926_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.57 do 0 intro. intros zenon_H18a zenon_H46 zenon_H150 zenon_Hf6 zenon_H14b zenon_H8b zenon_H186 zenon_H104 zenon_H67. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H133 | zenon_intro zenon_H18b ]. % 10.36/10.57 apply (zenon_L565_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H175 | zenon_intro zenon_H18c ]. % 10.36/10.57 apply (zenon_L124_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H187 | zenon_intro zenon_H189 ]. % 10.36/10.57 apply (zenon_L125_); trivial. % 10.36/10.57 apply (zenon_L286_); trivial. % 10.36/10.57 (* end of lemma zenon_L926_ *) % 10.36/10.57 assert (zenon_L927_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e0) (e0)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> False). % 10.36/10.57 do 0 intro. intros zenon_H2db zenon_H31 zenon_H119 zenon_Hc3 zenon_H154 zenon_Hcd zenon_H27c zenon_Hfd zenon_H67. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H136 | zenon_intro zenon_H2dc ]. % 10.36/10.57 apply (zenon_L202_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H252 | zenon_intro zenon_H2dd ]. % 10.36/10.57 apply (zenon_L333_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H2d9 | zenon_intro zenon_Hd3 ]. % 10.36/10.57 apply (zenon_L401_); trivial. % 10.36/10.57 apply (zenon_L353_); trivial. % 10.36/10.57 (* end of lemma zenon_L927_ *) % 10.36/10.57 assert (zenon_L928_ : (((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0)))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H1b7 zenon_H1a3 zenon_Hf4 zenon_H100 zenon_H2ed zenon_H67 zenon_Hfd zenon_Ha3 zenon_H2db zenon_H154 zenon_H27c zenon_H12a zenon_H56 zenon_H85. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H163. zenon_intro zenon_H2e. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.57 apply (zenon_L57_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.57 apply (zenon_L281_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.57 apply (zenon_L927_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.57 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.57 apply (zenon_L73_); trivial. % 10.36/10.57 apply (zenon_L881_); trivial. % 10.36/10.57 apply (zenon_L663_); trivial. % 10.36/10.57 (* end of lemma zenon_L928_ *) % 10.36/10.57 assert (zenon_L929_ : (((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1)))))) -> (~((op (e1) (e1)) = (e3))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H1cf zenon_Ha3. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_Hd4. zenon_intro zenon_H1d0. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_Hff. zenon_intro zenon_Hf2. % 10.36/10.57 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.36/10.57 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.57 (* end of lemma zenon_L929_ *) % 10.36/10.57 assert (zenon_L930_ : ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H56 zenon_H2e7 zenon_H67 zenon_H104 zenon_H284 zenon_Hfd zenon_Ha3 zenon_Hb3 zenon_H171 zenon_H177 zenon_H85 zenon_H298 zenon_H24b zenon_Hc6 zenon_H29d zenon_H266 zenon_H202 zenon_H2cd zenon_H2ed zenon_H26e zenon_H2ea zenon_H2c5 zenon_H1cb zenon_Hf4 zenon_H316 zenon_He9 zenon_H138 zenon_H320 zenon_H99 zenon_He0 zenon_H2a8 zenon_H14b zenon_H186 zenon_H18a zenon_Hda zenon_H1a2 zenon_H157 zenon_Hca zenon_H100 zenon_H12a zenon_H154 zenon_H27c zenon_H2db zenon_H1a3. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_Hff | zenon_intro zenon_Hd4 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.57 apply (zenon_L1_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.57 apply (zenon_L2_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.57 apply (zenon_L3_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.57 apply (zenon_L4_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.57 apply (zenon_L5_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.57 apply (zenon_L6_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.57 apply (zenon_L911_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.57 apply (zenon_L865_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.57 apply (zenon_L10_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.57 apply (zenon_L912_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.57 apply (zenon_L13_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.57 apply (zenon_L607_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.57 apply (zenon_L15_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.57 apply (zenon_L908_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.57 apply (zenon_L874_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.57 apply (zenon_L875_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.57 apply (zenon_L20_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.57 apply (zenon_L21_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H70). zenon_intro zenon_H6a. zenon_intro zenon_H72. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H6b. zenon_intro zenon_H27. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.36/10.57 apply (zenon_L921_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.57 apply (zenon_L857_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.57 apply (zenon_L24_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.57 apply (zenon_L25_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.57 apply (zenon_L26_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.57 apply (zenon_L27_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8c. zenon_intro zenon_H43. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.57 apply (zenon_L57_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H150 | zenon_intro zenon_H2a9 ]. % 10.36/10.57 apply (zenon_L926_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H17a | zenon_intro zenon_H2aa ]. % 10.36/10.57 apply (zenon_L118_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1ed ]. % 10.36/10.57 exact (zenon_Hff zenon_Hfc). % 10.36/10.57 apply (zenon_L387_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.57 apply (zenon_L131_); trivial. % 10.36/10.57 apply (zenon_L670_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.57 apply (zenon_L31_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.57 apply (zenon_L32_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.57 apply (zenon_L357_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.57 apply (zenon_L913_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.57 apply (zenon_L56_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.57 apply (zenon_L879_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.57 apply (zenon_L880_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.57 apply (zenon_L148_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_Hb9. zenon_intro zenon_H1ad. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H71. zenon_intro zenon_H24. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.36/10.57 apply (zenon_L884_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.57 apply (zenon_L150_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.57 apply (zenon_L692_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.57 apply (zenon_L928_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.57 apply (zenon_L154_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.57 apply (zenon_L155_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.57 apply (zenon_L885_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.57 apply (zenon_L157_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.57 apply (zenon_L158_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.57 apply (zenon_L159_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.57 apply (zenon_L160_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.57 apply (zenon_L916_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.57 apply (zenon_L929_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.57 apply (zenon_L164_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.57 apply (zenon_L888_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.57 apply (zenon_L166_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.57 apply (zenon_L889_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.57 apply (zenon_L890_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.57 apply (zenon_L169_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.57 apply (zenon_L891_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.57 apply (zenon_L172_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.57 apply (zenon_L892_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.57 apply (zenon_L174_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.57 apply (zenon_L523_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.57 apply (zenon_L388_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.57 apply (zenon_L178_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.57 apply (zenon_L179_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.57 apply (zenon_L893_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.57 apply (zenon_L894_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.57 apply (zenon_L895_); trivial. % 10.36/10.57 apply (zenon_L896_); trivial. % 10.36/10.57 apply (zenon_L920_); trivial. % 10.36/10.57 (* end of lemma zenon_L930_ *) % 10.36/10.57 assert (zenon_L931_ : (((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0)))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e2)) = (e0))\/(((op (e0) (e2)) = (e1))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e0)) = (e1))\/(((op (e3) (e0)) = (e2))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e3)) = (e0))\/(((op (e1) (e3)) = (e1))\/(((op (e1) (e3)) = (e2))\/((op (e1) (e3)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e0) (e0)) = (e0))/\((~((op (e0) (e0)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e0) (e1)) = (e0))/\((~((op (e0) (e0)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e0) (e2)) = (e0))/\((~((op (e0) (e0)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e0) (e3)) = (e0))/\((~((op (e0) (e0)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e1) (e0)) = (e1))/\((~((op (e1) (e1)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e1) (e1)) = (e1))/\((~((op (e1) (e1)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e1) (e2)) = (e1))/\((~((op (e1) (e1)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e1) (e3)) = (e1))/\((~((op (e1) (e1)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e2) (e0)) = (e2))/\((~((op (e2) (e2)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e2) (e1)) = (e2))/\((~((op (e2) (e2)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e2) (e2)) = (e2))/\((~((op (e2) (e2)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/((((op (e2) (e3)) = (e2))/\((~((op (e2) (e2)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e1) (e1)) = (e0))/\(~((op (e1) (e0)) = (e1))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e2) (e2)) = (e0))/\(~((op (e2) (e0)) = (e2))))))\/((((op (e3) (e0)) = (e3))/\((~((op (e3) (e3)) = (e0)))/\(((op (e3) (e3)) = (e0))/\(~((op (e3) (e0)) = (e3))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e0) (e0)) = (e1))/\(~((op (e0) (e1)) = (e0))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e2) (e2)) = (e1))/\(~((op (e2) (e1)) = (e2))))))\/((((op (e3) (e1)) = (e3))/\((~((op (e3) (e3)) = (e1)))/\(((op (e3) (e3)) = (e1))/\(~((op (e3) (e1)) = (e3))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e0) (e0)) = (e2))/\(~((op (e0) (e2)) = (e0))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e1) (e1)) = (e2))/\(~((op (e1) (e2)) = (e1))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))))\/((((op (e3) (e2)) = (e3))/\((~((op (e3) (e3)) = (e2)))/\(((op (e3) (e3)) = (e2))/\(~((op (e3) (e2)) = (e3))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e0) (e0)) = (e3))/\(~((op (e0) (e3)) = (e0))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e1) (e1)) = (e3))/\(~((op (e1) (e3)) = (e1))))))\/((((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e2) (e2)) = (e3))/\(~((op (e2) (e3)) = (e2))))))\/(((op (e3) (e3)) = (e3))/\((~((op (e3) (e3)) = (e3)))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e2))\/(((op (e2) (e1)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e2) (e1)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H89 zenon_H308 zenon_H130 zenon_H2bc zenon_H145 zenon_H17e zenon_H9c zenon_H173 zenon_H2e7 zenon_H67 zenon_H104 zenon_H284 zenon_Hfd zenon_Ha3 zenon_Hb3 zenon_H171 zenon_H177 zenon_H85 zenon_H298 zenon_H24b zenon_Hc6 zenon_H29d zenon_H266 zenon_H202 zenon_H2cd zenon_H2ed zenon_H26e zenon_H2ea zenon_H2c5 zenon_H1cb zenon_Hf4 zenon_H316 zenon_He9 zenon_H138 zenon_H320 zenon_H99 zenon_He0 zenon_H2a8 zenon_H14b zenon_H186 zenon_H18a zenon_Hda zenon_H1a2 zenon_H157 zenon_Hca zenon_H100 zenon_H12a zenon_H154 zenon_H27c zenon_H2db zenon_H1a3. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H8a). zenon_intro zenon_H8c. zenon_intro zenon_H43. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2db); [ zenon_intro zenon_H136 | zenon_intro zenon_H2dc ]. % 10.36/10.57 apply (zenon_L726_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2dc); [ zenon_intro zenon_H252 | zenon_intro zenon_H2dd ]. % 10.36/10.57 apply (zenon_L923_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2dd); [ zenon_intro zenon_H2d9 | zenon_intro zenon_Hd3 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H131 | zenon_intro zenon_H146 ]. % 10.36/10.57 apply (zenon_L81_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H133 | zenon_intro zenon_H147 ]. % 10.36/10.57 apply (zenon_L924_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H136 | zenon_intro zenon_H13b ]. % 10.36/10.57 apply (zenon_L726_); trivial. % 10.36/10.57 apply (zenon_L221_); trivial. % 10.36/10.57 apply (zenon_L353_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.57 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.57 apply (zenon_L118_); trivial. % 10.36/10.57 apply (zenon_L395_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.57 apply (zenon_L925_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.57 exact (zenon_H45 zenon_H42). % 10.36/10.57 apply (zenon_L930_); trivial. % 10.36/10.57 (* end of lemma zenon_L931_ *) % 10.36/10.57 assert (zenon_L932_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> False). % 10.36/10.57 do 0 intro. intros zenon_H290 zenon_H241 zenon_H278 zenon_H163 zenon_Hc3 zenon_H2a5 zenon_Hff. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H74 | zenon_intro zenon_H291 ]. % 10.36/10.57 apply (zenon_L298_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H103 | zenon_intro zenon_H292 ]. % 10.36/10.57 exact (zenon_H163 zenon_H103). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfc ]. % 10.36/10.57 apply (zenon_L287_); trivial. % 10.36/10.57 exact (zenon_Hff zenon_Hfc). % 10.36/10.57 (* end of lemma zenon_L932_ *) % 10.36/10.57 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H303. zenon_intro zenon_H321. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H321). zenon_intro zenon_H2e0. zenon_intro zenon_H322. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H322). zenon_intro zenon_H2bc. zenon_intro zenon_H323. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H323). zenon_intro zenon_H269. zenon_intro zenon_H324. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H324). zenon_intro zenon_H142. zenon_intro zenon_H325. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H325). zenon_intro zenon_Hb3. zenon_intro zenon_H326. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H326). zenon_intro zenon_H31c. zenon_intro zenon_H327. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H327). zenon_intro zenon_H266. zenon_intro zenon_H328. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H328). zenon_intro zenon_H28c. zenon_intro zenon_H329. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H329). zenon_intro zenon_H2d6. zenon_intro zenon_H32a. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H32a). zenon_intro zenon_H290. zenon_intro zenon_H32b. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H32b). zenon_intro zenon_H32d. zenon_intro zenon_H32c. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H32c). zenon_intro zenon_H145. zenon_intro zenon_H32e. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H32e). zenon_intro zenon_H2f2. zenon_intro zenon_H32f. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H32f). zenon_intro zenon_H318. zenon_intro zenon_H2cf. % 10.36/10.57 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H308. zenon_intro zenon_H330. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H330). zenon_intro zenon_H30e. zenon_intro zenon_H331. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H331). zenon_intro zenon_H1a2. zenon_intro zenon_H332. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H332). zenon_intro zenon_H191. zenon_intro zenon_H333. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H333). zenon_intro zenon_H1a3. zenon_intro zenon_H334. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H334). zenon_intro zenon_H281. zenon_intro zenon_H335. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H335). zenon_intro zenon_H15e. zenon_intro zenon_H336. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H336). zenon_intro zenon_H289. zenon_intro zenon_H337. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H337). zenon_intro zenon_Hb6. zenon_intro zenon_H338. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H338). zenon_intro zenon_H12d. zenon_intro zenon_H339. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H339). zenon_intro zenon_H2ab. zenon_intro zenon_H33a. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H33a). zenon_intro zenon_H24e. zenon_intro zenon_H33b. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H33b). zenon_intro zenon_Hdf. zenon_intro zenon_H33c. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H33c). zenon_intro zenon_H2b9. zenon_intro zenon_H33d. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H33d). zenon_intro zenon_H17e. zenon_intro zenon_H33e. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H33e). zenon_intro zenon_H12a. zenon_intro zenon_H33f. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H33f). zenon_intro zenon_Hca. zenon_intro zenon_H340. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H340). zenon_intro zenon_H2ae. zenon_intro zenon_H341. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H341). zenon_intro zenon_H124. zenon_intro zenon_H342. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H342). zenon_intro zenon_H293. zenon_intro zenon_H343. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H343). zenon_intro zenon_He0. zenon_intro zenon_H344. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H344). zenon_intro zenon_H346. zenon_intro zenon_H345. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H345). zenon_intro zenon_H15b. zenon_intro zenon_H347. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H347). zenon_intro zenon_H2a8. zenon_intro zenon_H348. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H348). zenon_intro zenon_H245. zenon_intro zenon_H349. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H349). zenon_intro zenon_H272. zenon_intro zenon_H34a. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H34a). zenon_intro zenon_H18a. zenon_intro zenon_H34b. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H34b). zenon_intro zenon_H298. zenon_intro zenon_H34c. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H34c). zenon_intro zenon_H2db. zenon_intro zenon_H34d. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H34d). zenon_intro zenon_H2c5. zenon_intro zenon_H34e. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H34e). zenon_intro zenon_H244. zenon_intro zenon_H2d3. % 10.36/10.57 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H94. zenon_intro zenon_H34f. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H34f). zenon_intro zenon_Hc0. zenon_intro zenon_H350. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H350). zenon_intro zenon_H130. zenon_intro zenon_H351. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H351). zenon_intro zenon_Hbb. zenon_intro zenon_H352. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H352). zenon_intro zenon_H13d. zenon_intro zenon_H353. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H353). zenon_intro zenon_H135. zenon_intro zenon_H354. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H354). zenon_intro zenon_H173. zenon_intro zenon_H355. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H355). zenon_intro zenon_H100. zenon_intro zenon_H356. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H356). zenon_intro zenon_H14b. zenon_intro zenon_H357. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H357). zenon_intro zenon_H171. zenon_intro zenon_H358. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H358). zenon_intro zenon_H262. zenon_intro zenon_H359. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H359). zenon_intro zenon_H154. zenon_intro zenon_H35a. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H35a). zenon_intro zenon_Hda. zenon_intro zenon_H35b. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H35b). zenon_intro zenon_Hce. zenon_intro zenon_H35c. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H35c). zenon_intro zenon_H27c. zenon_intro zenon_H35d. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H35d). zenon_intro zenon_H182. zenon_intro zenon_H35e. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H35e). zenon_intro zenon_H186. zenon_intro zenon_H35f. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H35f). zenon_intro zenon_H278. zenon_intro zenon_H360. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H360). zenon_intro zenon_H24b. zenon_intro zenon_H361. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H361). zenon_intro zenon_H157. zenon_intro zenon_H362. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H362). zenon_intro zenon_He6. zenon_intro zenon_H363. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H363). zenon_intro zenon_Hc6. zenon_intro zenon_H364. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H364). zenon_intro zenon_H29d. zenon_intro zenon_H365. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H365). zenon_intro zenon_Hd5. zenon_intro zenon_H366. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H366). zenon_intro zenon_H37. zenon_intro zenon_H367. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H367). zenon_intro zenon_H47. zenon_intro zenon_H368. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H368). zenon_intro zenon_H5b. zenon_intro zenon_H369. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H369). zenon_intro zenon_H2e4. zenon_intro zenon_H36a. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H36a). zenon_intro zenon_H2e7. zenon_intro zenon_H36b. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H36b). zenon_intro zenon_H284. zenon_intro zenon_H36c. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H36c). zenon_intro zenon_H177. zenon_intro zenon_H36d. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H36d). zenon_intro zenon_H18d. zenon_intro zenon_H36e. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H36e). zenon_intro zenon_H138. zenon_intro zenon_H36f. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H36f). zenon_intro zenon_H9c. zenon_intro zenon_H370. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H370). zenon_intro zenon_H115. zenon_intro zenon_H371. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H371). zenon_intro zenon_H316. zenon_intro zenon_H372. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H372). zenon_intro zenon_H1b2. zenon_intro zenon_H373. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H373). zenon_intro zenon_H287. zenon_intro zenon_H374. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H374). zenon_intro zenon_H1cb. zenon_intro zenon_H375. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H375). zenon_intro zenon_H2a5. zenon_intro zenon_H376. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H376). zenon_intro zenon_H2ea. zenon_intro zenon_H377. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H377). zenon_intro zenon_H28f. zenon_intro zenon_H378. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H378). zenon_intro zenon_H1de. zenon_intro zenon_H379. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H379). zenon_intro zenon_H1ef. zenon_intro zenon_H37a. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H37a). zenon_intro zenon_H26e. zenon_intro zenon_H37b. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H37b). zenon_intro zenon_H2ef. zenon_intro zenon_H37c. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H37c). zenon_intro zenon_H2ed. zenon_intro zenon_H2cd. % 10.36/10.57 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H99. zenon_intro zenon_H37d. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H37d). zenon_intro zenon_H85. zenon_intro zenon_H37e. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_He9. zenon_intro zenon_H37f. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H37f). zenon_intro zenon_Hf4. zenon_intro zenon_H380. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H380). zenon_intro zenon_H104. zenon_intro zenon_Hfd. % 10.36/10.57 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H381. zenon_intro zenon_H202. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H381); [ zenon_intro zenon_H383 | zenon_intro zenon_H382 ]. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H383). zenon_intro zenon_H1f. zenon_intro zenon_H384. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H384). zenon_intro zenon_H386. zenon_intro zenon_H385. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H385). zenon_intro zenon_H388. zenon_intro zenon_H387. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H387). zenon_intro zenon_H29b. zenon_intro zenon_H29c. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H388); [ zenon_intro zenon_H6b | zenon_intro zenon_H6a ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H29b); [ zenon_intro zenon_H71 | zenon_intro zenon_Hb9 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H29c); [ zenon_intro zenon_H76 | zenon_intro zenon_H13b ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.57 apply (zenon_L1_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.57 apply (zenon_L2_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.57 apply (zenon_L3_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.57 apply (zenon_L4_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.57 apply (zenon_L5_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.57 apply (zenon_L6_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.57 apply (zenon_L8_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.57 apply (zenon_L9_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.57 apply (zenon_L10_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.57 apply (zenon_L12_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.57 apply (zenon_L13_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.57 apply (zenon_L14_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.57 apply (zenon_L15_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.57 apply (zenon_L17_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.57 apply (zenon_L18_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.57 apply (zenon_L19_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.57 apply (zenon_L20_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.57 apply (zenon_L21_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.57 apply (zenon_L22_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.57 apply (zenon_L23_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.57 apply (zenon_L24_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.57 apply (zenon_L25_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.57 apply (zenon_L26_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.57 apply (zenon_L27_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.57 apply (zenon_L30_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.57 apply (zenon_L31_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.57 apply (zenon_L32_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H18f). zenon_intro zenon_H8b. zenon_intro zenon_H190. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H190). zenon_intro zenon_H8c. zenon_intro zenon_H1c8. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.57 apply (zenon_L29_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.57 apply (zenon_L42_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.57 apply (zenon_L52_); trivial. % 10.36/10.57 apply (zenon_L53_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.57 apply (zenon_L55_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.57 apply (zenon_L56_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H16f). zenon_intro zenon_Hef. zenon_intro zenon_H170. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H170). zenon_intro zenon_Ha3. zenon_intro zenon_H1d3. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.57 apply (zenon_L57_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.36/10.57 apply (zenon_L33_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.36/10.57 exact (zenon_H6b zenon_H6f). % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.57 apply (zenon_L7_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.57 exact (zenon_H6b zenon_H6f). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.36/10.57 apply (zenon_L80_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.36/10.57 apply (zenon_L65_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.36/10.57 apply (zenon_L194_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.57 apply (zenon_L196_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.57 apply (zenon_L197_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.57 apply (zenon_L45_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.57 apply (zenon_L72_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.57 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.57 apply (zenon_L198_); trivial. % 10.36/10.57 apply (zenon_L199_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.36/10.57 apply (zenon_L78_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.36/10.57 apply (zenon_L106_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.36/10.57 apply (zenon_L194_); trivial. % 10.36/10.57 apply (zenon_L111_); trivial. % 10.36/10.57 apply (zenon_L71_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.57 apply (zenon_L192_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.36/10.57 apply (zenon_L33_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.36/10.57 exact (zenon_H6b zenon_H6f). % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.36/10.57 apply (zenon_L79_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.36/10.57 apply (zenon_L65_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.36/10.57 apply (zenon_L194_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.57 apply (zenon_L202_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.57 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.57 apply (zenon_L198_); trivial. % 10.36/10.57 apply (zenon_L187_); trivial. % 10.36/10.57 apply (zenon_L71_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.57 apply (zenon_L80_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.57 apply (zenon_L205_); trivial. % 10.36/10.57 apply (zenon_L191_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.57 apply (zenon_L147_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.57 apply (zenon_L148_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.57 apply (zenon_L149_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.57 apply (zenon_L150_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.57 apply (zenon_L206_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H163. zenon_intro zenon_H2e. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.36/10.57 apply (zenon_L33_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.36/10.57 exact (zenon_H6b zenon_H6f). % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.57 exact (zenon_H30 zenon_H2d). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.57 exact (zenon_H6b zenon_H6f). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.57 apply (zenon_L45_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.36/10.57 apply (zenon_L207_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.57 apply (zenon_L224_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.57 apply (zenon_L225_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.57 apply (zenon_L73_); trivial. % 10.36/10.57 apply (zenon_L77_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.36/10.57 apply (zenon_L35_); trivial. % 10.36/10.57 apply (zenon_L227_); trivial. % 10.36/10.57 apply (zenon_L47_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.57 apply (zenon_L154_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.57 apply (zenon_L155_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_Hc3. zenon_intro zenon_H1bf. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H163. zenon_intro zenon_H83. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.36/10.57 apply (zenon_L33_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.36/10.57 exact (zenon_H6b zenon_H6f). % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.36/10.57 apply (zenon_L115_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.36/10.57 apply (zenon_L228_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.36/10.57 apply (zenon_L35_); trivial. % 10.36/10.57 apply (zenon_L226_); trivial. % 10.36/10.57 apply (zenon_L47_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.36/10.57 apply (zenon_L33_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.36/10.57 exact (zenon_H6b zenon_H6f). % 10.36/10.57 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.57 apply (zenon_L7_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.57 exact (zenon_H6b zenon_H6f). % 10.36/10.57 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.57 apply (zenon_L45_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.36/10.57 apply (zenon_L278_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.36/10.57 apply (zenon_L279_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.36/10.57 apply (zenon_L35_); trivial. % 10.36/10.57 apply (zenon_L280_); trivial. % 10.36/10.57 apply (zenon_L47_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.57 apply (zenon_L29_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.57 apply (zenon_L281_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.57 apply (zenon_L189_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.57 apply (zenon_L54_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.57 apply (zenon_L291_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.57 apply (zenon_L105_); trivial. % 10.36/10.57 apply (zenon_L103_); trivial. % 10.36/10.57 apply (zenon_L140_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.57 apply (zenon_L157_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.57 apply (zenon_L158_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.57 apply (zenon_L159_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.57 apply (zenon_L160_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.57 apply (zenon_L233_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_Hd4. zenon_intro zenon_H1d0. % 10.36/10.57 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_Hff. zenon_intro zenon_Hf2. % 10.36/10.57 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.57 apply (zenon_L29_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.57 apply (zenon_L235_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.57 apply (zenon_L294_); trivial. % 10.36/10.57 apply (zenon_L240_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.57 apply (zenon_L164_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.57 apply (zenon_L165_); trivial. % 10.36/10.57 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.58 apply (zenon_L166_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.58 apply (zenon_L167_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.58 apply (zenon_L242_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.58 apply (zenon_L169_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H127. zenon_intro zenon_H1e2. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H1e5. zenon_intro zenon_H2e. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 apply (zenon_L57_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L295_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L90_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L315_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.58 apply (zenon_L295_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.58 apply (zenon_L332_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.58 apply (zenon_L301_); trivial. % 10.36/10.58 apply (zenon_L465_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L54_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L90_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L91_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.58 apply (zenon_L54_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.58 apply (zenon_L471_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.58 apply (zenon_L474_); trivial. % 10.36/10.58 apply (zenon_L171_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L54_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L90_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L483_); trivial. % 10.36/10.58 apply (zenon_L103_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.58 apply (zenon_L172_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H127. zenon_intro zenon_H1e7. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1e5. zenon_intro zenon_H80. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 apply (zenon_L29_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 apply (zenon_L29_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L295_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L90_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L364_); trivial. % 10.36/10.58 apply (zenon_L485_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L365_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L54_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L202_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L364_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 apply (zenon_L486_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 exact (zenon_H6b zenon_H6f). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.36/10.58 apply (zenon_L83_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.36/10.58 exact (zenon_H1bd zenon_Hc3). % 10.36/10.58 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.36/10.58 apply (zenon_L302_); trivial. % 10.36/10.58 apply (zenon_L326_); trivial. % 10.36/10.58 apply (zenon_L77_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L295_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L90_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L364_); trivial. % 10.36/10.58 apply (zenon_L487_); trivial. % 10.36/10.58 apply (zenon_L488_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 apply (zenon_L29_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L54_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L99_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L364_); trivial. % 10.36/10.58 apply (zenon_L487_); trivial. % 10.36/10.58 apply (zenon_L488_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_L366_); trivial. % 10.36/10.58 apply (zenon_L367_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.58 apply (zenon_L174_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.58 apply (zenon_L246_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H1ed. zenon_intro zenon_H1f4. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1f4). zenon_intro zenon_H1ee. zenon_intro zenon_H8f. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 apply (zenon_L29_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_L108_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L490_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 apply (zenon_L29_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_L197_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L393_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L385_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L202_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L252_); trivial. % 10.36/10.58 apply (zenon_L103_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 apply (zenon_L29_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_L108_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L490_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 apply (zenon_L29_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_L197_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L450_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L385_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L99_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L252_); trivial. % 10.36/10.58 apply (zenon_L103_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 apply (zenon_L29_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_L108_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L189_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L390_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L371_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L105_); trivial. % 10.36/10.58 apply (zenon_L103_); trivial. % 10.36/10.58 apply (zenon_L453_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.58 apply (zenon_L178_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.58 apply (zenon_L179_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.58 apply (zenon_L180_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.58 apply (zenon_L181_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.58 apply (zenon_L182_); trivial. % 10.36/10.58 apply (zenon_L183_); trivial. % 10.36/10.58 apply (zenon_L465_); trivial. % 10.36/10.58 apply (zenon_L454_); trivial. % 10.36/10.58 apply (zenon_L278_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H382); [ zenon_intro zenon_H38a | zenon_intro zenon_H389 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H38a). zenon_intro zenon_H36. zenon_intro zenon_H38b. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H38b). zenon_intro zenon_H38d. zenon_intro zenon_H38c. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H38c). zenon_intro zenon_H38f. zenon_intro zenon_H38e. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H38e). zenon_intro zenon_H302. zenon_intro zenon_H2f5. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H38d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2d ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H302); [ zenon_intro zenon_H163 | zenon_intro zenon_Hc3 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H1e5 | zenon_intro zenon_H127 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.58 apply (zenon_L1_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.58 apply (zenon_L2_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.58 apply (zenon_L3_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.58 apply (zenon_L4_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.58 apply (zenon_L5_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.58 apply (zenon_L6_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.58 apply (zenon_L491_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.58 apply (zenon_L492_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.58 apply (zenon_L10_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.58 apply (zenon_L493_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.58 apply (zenon_L13_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H42. zenon_intro zenon_H53. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H44. zenon_intro zenon_H1c8. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1c8). zenon_intro zenon_Hd3. zenon_intro zenon_H1f9. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H1f | zenon_intro zenon_H30f ]. % 10.36/10.58 apply (zenon_L11_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H95 | zenon_intro zenon_H310 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.58 apply (zenon_L394_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 apply (zenon_L604_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.58 apply (zenon_L197_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.58 apply (zenon_L45_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.58 apply (zenon_L359_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.58 apply (zenon_L225_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.58 apply (zenon_L621_); trivial. % 10.36/10.58 apply (zenon_L646_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.58 apply (zenon_L310_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.58 apply (zenon_L618_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.58 apply (zenon_L359_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.58 apply (zenon_L225_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.58 apply (zenon_L621_); trivial. % 10.36/10.58 apply (zenon_L645_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L99_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L91_); trivial. % 10.36/10.58 apply (zenon_L647_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L59_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 apply (zenon_L58_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.58 apply (zenon_L197_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.58 apply (zenon_L618_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.58 apply (zenon_L359_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.58 apply (zenon_L225_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.58 apply (zenon_L648_); trivial. % 10.36/10.58 apply (zenon_L649_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.58 apply (zenon_L310_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.58 apply (zenon_L50_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.58 apply (zenon_L310_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.58 apply (zenon_L611_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.58 apply (zenon_L359_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.58 apply (zenon_L137_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.58 apply (zenon_L648_); trivial. % 10.36/10.58 apply (zenon_L646_); trivial. % 10.36/10.58 apply (zenon_L610_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L99_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L616_); trivial. % 10.36/10.58 apply (zenon_L650_); trivial. % 10.36/10.58 apply (zenon_L629_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.58 apply (zenon_L630_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.58 apply (zenon_L614_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.58 apply (zenon_L322_); trivial. % 10.36/10.58 apply (zenon_L624_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_L421_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.58 apply (zenon_L282_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L541_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.58 apply (zenon_L541_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.58 apply (zenon_L640_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.58 apply (zenon_L354_); trivial. % 10.36/10.58 apply (zenon_L609_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L616_); trivial. % 10.36/10.58 apply (zenon_L135_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L59_); trivial. % 10.36/10.58 apply (zenon_L651_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L653_); trivial. % 10.36/10.58 apply (zenon_L143_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L541_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.58 apply (zenon_L541_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.58 apply (zenon_L640_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.58 apply (zenon_L354_); trivial. % 10.36/10.58 apply (zenon_L123_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L616_); trivial. % 10.36/10.58 apply (zenon_L135_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L633_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 apply (zenon_L604_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.58 apply (zenon_L651_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.58 apply (zenon_L637_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.58 exact (zenon_H163 zenon_H103). % 10.36/10.58 apply (zenon_L210_); trivial. % 10.36/10.58 apply (zenon_L614_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.58 apply (zenon_L640_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.58 apply (zenon_L225_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.36/10.58 apply (zenon_L59_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.36/10.58 apply (zenon_L613_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.36/10.58 apply (zenon_L655_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.58 apply (zenon_L628_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.58 apply (zenon_L610_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.58 apply (zenon_L566_); trivial. % 10.36/10.58 apply (zenon_L624_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.58 apply (zenon_L107_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.58 exact (zenon_H163 zenon_H103). % 10.36/10.58 apply (zenon_L210_); trivial. % 10.36/10.58 apply (zenon_L649_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.58 apply (zenon_L640_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.58 apply (zenon_L354_); trivial. % 10.36/10.58 apply (zenon_L609_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L616_); trivial. % 10.36/10.58 apply (zenon_L135_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L653_); trivial. % 10.36/10.58 apply (zenon_L143_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H131 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.58 apply (zenon_L282_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 apply (zenon_L494_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_L259_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.58 apply (zenon_L197_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.58 apply (zenon_L279_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.58 apply (zenon_L359_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.58 apply (zenon_L225_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.58 apply (zenon_L99_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.58 apply (zenon_L225_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.36/10.58 apply (zenon_L417_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.36/10.58 apply (zenon_L73_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.36/10.58 apply (zenon_L48_); trivial. % 10.36/10.58 apply (zenon_L620_); trivial. % 10.36/10.58 apply (zenon_L199_); trivial. % 10.36/10.58 apply (zenon_L645_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L99_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L91_); trivial. % 10.36/10.58 apply (zenon_L647_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L59_); trivial. % 10.36/10.58 apply (zenon_L656_); trivial. % 10.36/10.58 apply (zenon_L629_); trivial. % 10.36/10.58 apply (zenon_L657_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_L421_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.58 apply (zenon_L282_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.58 apply (zenon_L541_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.58 apply (zenon_L640_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.58 apply (zenon_L658_); trivial. % 10.36/10.58 apply (zenon_L659_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L417_); trivial. % 10.36/10.58 apply (zenon_L656_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_L642_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L59_); trivial. % 10.36/10.58 apply (zenon_L656_); trivial. % 10.36/10.58 apply (zenon_L143_); trivial. % 10.36/10.58 apply (zenon_L657_); trivial. % 10.36/10.58 apply (zenon_L644_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.58 apply (zenon_L15_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.58 apply (zenon_L660_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H56. zenon_intro zenon_H62. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H58. zenon_intro zenon_H1d3. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1d3). zenon_intro zenon_Hfc. zenon_intro zenon_H122. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.58 apply (zenon_L282_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.58 apply (zenon_L310_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.58 apply (zenon_L605_); trivial. % 10.36/10.58 apply (zenon_L661_); trivial. % 10.36/10.58 apply (zenon_L664_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.58 exact (zenon_H58 zenon_H5a). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.58 apply (zenon_L665_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.58 apply (zenon_L668_); trivial. % 10.36/10.58 apply (zenon_L669_); trivial. % 10.36/10.58 apply (zenon_L670_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.58 apply (zenon_L19_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.58 apply (zenon_L20_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.58 apply (zenon_L21_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.58 apply (zenon_L499_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.58 apply (zenon_L500_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.58 apply (zenon_L24_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.58 apply (zenon_L25_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.58 apply (zenon_L26_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.58 apply (zenon_L27_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.58 apply (zenon_L501_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.58 apply (zenon_L31_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.58 apply (zenon_L32_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.58 apply (zenon_L502_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.58 apply (zenon_L503_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.58 apply (zenon_L56_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.58 apply (zenon_L106_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.58 apply (zenon_L147_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.58 apply (zenon_L148_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.58 apply (zenon_L671_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.58 apply (zenon_L150_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_Hb9. zenon_intro zenon_H1b1. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1b1). zenon_intro zenon_H71. zenon_intro zenon_H2a. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.36/10.58 apply (zenon_L33_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_Hfa | zenon_intro zenon_H125 ]. % 10.36/10.58 apply (zenon_L59_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H101 | zenon_intro zenon_H126 ]. % 10.36/10.58 apply (zenon_L107_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H103 | zenon_intro zenon_H107 ]. % 10.36/10.58 exact (zenon_H163 zenon_H103). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H74 | zenon_intro zenon_H291 ]. % 10.36/10.58 exact (zenon_H71 zenon_H74). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H103 | zenon_intro zenon_H292 ]. % 10.36/10.58 exact (zenon_H163 zenon_H103). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfc ]. % 10.36/10.58 apply (zenon_L672_); trivial. % 10.36/10.58 apply (zenon_L64_); trivial. % 10.36/10.58 apply (zenon_L579_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.58 apply (zenon_L507_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H293); [ zenon_intro zenon_H16e | zenon_intro zenon_H294 ]. % 10.36/10.58 apply (zenon_L421_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H294); [ zenon_intro zenon_H8b | zenon_intro zenon_H295 ]. % 10.36/10.58 apply (zenon_L36_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H295); [ zenon_intro zenon_H103 | zenon_intro zenon_H187 ]. % 10.36/10.58 exact (zenon_H163 zenon_H103). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.36/10.58 exact (zenon_H78 zenon_H13b). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.36/10.58 apply (zenon_L691_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.36/10.58 apply (zenon_L219_); trivial. % 10.36/10.58 apply (zenon_L692_); trivial. % 10.36/10.58 apply (zenon_L584_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.58 apply (zenon_L675_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.58 apply (zenon_L154_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.58 apply (zenon_L155_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.58 apply (zenon_L510_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.58 apply (zenon_L157_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.58 apply (zenon_L158_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.58 apply (zenon_L159_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.58 apply (zenon_L160_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_Hd4. zenon_intro zenon_H1ca. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1ca). zenon_intro zenon_Hff. zenon_intro zenon_H57. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.36/10.58 apply (zenon_L33_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.36/10.58 apply (zenon_L694_); trivial. % 10.36/10.58 apply (zenon_L696_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L699_); trivial. % 10.36/10.58 apply (zenon_L240_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.58 apply (zenon_L359_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.58 apply (zenon_L225_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H42 | zenon_intro zenon_H2af ]. % 10.36/10.58 apply (zenon_L421_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H9a | zenon_intro zenon_H2b0 ]. % 10.36/10.58 apply (zenon_L694_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H74 | zenon_intro zenon_H241 ]. % 10.36/10.58 apply (zenon_L703_); trivial. % 10.36/10.58 apply (zenon_L676_); trivial. % 10.36/10.58 apply (zenon_L551_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H95 | zenon_intro zenon_Hb7 ]. % 10.36/10.58 apply (zenon_L33_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H6f | zenon_intro zenon_Hb8 ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hb8); [ zenon_intro zenon_H9a | zenon_intro zenon_Ha5 ]. % 10.36/10.58 apply (zenon_L693_); trivial. % 10.36/10.58 apply (zenon_L705_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.58 apply (zenon_L604_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 apply (zenon_L494_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.58 apply (zenon_L511_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.58 apply (zenon_L310_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.58 apply (zenon_L310_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.58 apply (zenon_L45_); trivial. % 10.36/10.58 apply (zenon_L708_); trivial. % 10.36/10.58 apply (zenon_L238_); trivial. % 10.36/10.58 apply (zenon_L709_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L699_); trivial. % 10.36/10.58 apply (zenon_L240_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_L421_); trivial. % 10.36/10.58 apply (zenon_L688_); trivial. % 10.36/10.58 exact (zenon_H59 zenon_H56). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.58 apply (zenon_L292_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.58 apply (zenon_L164_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.58 apply (zenon_L165_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.58 apply (zenon_L166_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.58 apply (zenon_L518_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_H13b. zenon_intro zenon_H1db. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1db). zenon_intro zenon_H76. zenon_intro zenon_H27. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H74. zenon_intro zenon_H73. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.58 apply (zenon_L282_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 apply (zenon_L58_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_L713_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.58 apply (zenon_L85_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.58 apply (zenon_L225_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.58 apply (zenon_L702_); trivial. % 10.36/10.58 apply (zenon_L714_); trivial. % 10.36/10.58 apply (zenon_L123_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_L669_); trivial. % 10.36/10.58 apply (zenon_L715_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.58 apply (zenon_L169_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.58 apply (zenon_L690_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.58 apply (zenon_L172_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.58 apply (zenon_L577_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.58 apply (zenon_L174_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ed. zenon_intro zenon_H1ec. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1ec). zenon_intro zenon_H1ee. zenon_intro zenon_H43. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 exact (zenon_H2f zenon_H31). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 apply (zenon_L58_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.58 apply (zenon_L511_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.58 apply (zenon_L310_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.58 apply (zenon_L89_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.58 apply (zenon_L310_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.58 apply (zenon_L45_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.58 apply (zenon_L716_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.58 apply (zenon_L225_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.58 apply (zenon_L249_); trivial. % 10.36/10.58 apply (zenon_L736_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.58 apply (zenon_L716_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.58 apply (zenon_L137_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.58 apply (zenon_L249_); trivial. % 10.36/10.58 apply (zenon_L738_); trivial. % 10.36/10.58 apply (zenon_L526_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L742_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_L743_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_L105_); trivial. % 10.36/10.58 apply (zenon_L592_); trivial. % 10.36/10.58 apply (zenon_L600_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.58 apply (zenon_L369_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.58 apply (zenon_L178_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.58 apply (zenon_L179_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.58 apply (zenon_L180_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.58 apply (zenon_L181_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.58 apply (zenon_L182_); trivial. % 10.36/10.58 apply (zenon_L183_); trivial. % 10.36/10.58 apply (zenon_L691_); trivial. % 10.36/10.58 apply (zenon_L734_); trivial. % 10.36/10.58 apply (zenon_L604_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H389); [ zenon_intro zenon_H391 | zenon_intro zenon_H390 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H391). zenon_intro zenon_H51. zenon_intro zenon_H392. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H392). zenon_intro zenon_H394. zenon_intro zenon_H393. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H393). zenon_intro zenon_H396. zenon_intro zenon_H395. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H395). zenon_intro zenon_H397. zenon_intro zenon_H31f. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H394); [ zenon_intro zenon_H44 | zenon_intro zenon_H42 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H396); [ zenon_intro zenon_H8c | zenon_intro zenon_H8b ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1ed ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.58 apply (zenon_L1_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.58 apply (zenon_L2_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.58 apply (zenon_L3_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.58 apply (zenon_L4_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.58 apply (zenon_L5_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.58 apply (zenon_L6_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.58 apply (zenon_L744_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H2d. zenon_intro zenon_H3f. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H2f. zenon_intro zenon_H83. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H189. zenon_intro zenon_H1ea. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H13b | zenon_intro zenon_H248 ]. % 10.36/10.58 apply (zenon_L745_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H127 | zenon_intro zenon_H249 ]. % 10.36/10.58 exact (zenon_H1ea zenon_H127). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1ed | zenon_intro zenon_H67 ]. % 10.36/10.58 apply (zenon_L749_); trivial. % 10.36/10.58 apply (zenon_L286_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.58 apply (zenon_L10_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.58 apply (zenon_L750_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.58 apply (zenon_L13_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.58 apply (zenon_L751_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.58 apply (zenon_L15_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H5f). zenon_intro zenon_H56. zenon_intro zenon_H60. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H58. zenon_intro zenon_Hf2. % 10.36/10.58 apply (zenon_and_s _ _ zenon_Hf2). zenon_intro zenon_Ha2. zenon_intro zenon_Hf3. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.58 exact (zenon_H58 zenon_H5a). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.58 apply (zenon_L116_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.36/10.58 apply (zenon_L658_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.36/10.58 apply (zenon_L752_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.36/10.58 apply (zenon_L595_); trivial. % 10.36/10.58 apply (zenon_L209_); trivial. % 10.36/10.58 apply (zenon_L756_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L48_); trivial. % 10.36/10.58 apply (zenon_L663_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.58 apply (zenon_L666_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.58 apply (zenon_L19_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.58 apply (zenon_L20_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.58 apply (zenon_L21_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.58 apply (zenon_L757_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H6a. zenon_intro zenon_H77. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H6b. zenon_intro zenon_H2a. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_L758_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L48_); trivial. % 10.36/10.58 apply (zenon_L746_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.58 apply (zenon_L24_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.58 apply (zenon_L25_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.58 apply (zenon_L26_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.58 apply (zenon_L27_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.58 apply (zenon_L759_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.58 apply (zenon_L31_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.58 apply (zenon_L32_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.58 apply (zenon_L760_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_Hed). zenon_intro zenon_Hef. zenon_intro zenon_Hee. % 10.36/10.58 apply (zenon_and_s _ _ zenon_Hee). zenon_intro zenon_Ha3. zenon_intro zenon_H57. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.58 apply (zenon_L295_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.58 apply (zenon_L84_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.58 apply (zenon_L761_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 apply (zenon_L7_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.58 apply (zenon_L770_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.58 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.58 apply (zenon_L766_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.36/10.58 apply (zenon_L44_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.36/10.58 apply (zenon_L771_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.36/10.58 apply (zenon_L595_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.36/10.58 apply (zenon_L384_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.36/10.58 apply (zenon_L93_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.36/10.58 apply (zenon_L60_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.58 apply (zenon_L772_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.58 apply (zenon_L77_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2c5); [ zenon_intro zenon_He5 | zenon_intro zenon_H2c6 ]. % 10.36/10.58 apply (zenon_L774_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2c6); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2c7 ]. % 10.36/10.58 apply (zenon_L97_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2c7); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd3 ]. % 10.36/10.58 apply (zenon_L234_); trivial. % 10.36/10.58 exact (zenon_H1ee zenon_Hd3). % 10.36/10.58 apply (zenon_L506_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.58 exact (zenon_H8c zenon_H91). % 10.36/10.58 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.58 apply (zenon_L307_); trivial. % 10.36/10.58 apply (zenon_L97_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_L771_); trivial. % 10.36/10.58 apply (zenon_L768_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L48_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 apply (zenon_L775_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.36/10.58 apply (zenon_L777_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.58 apply (zenon_L770_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.58 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.58 apply (zenon_L765_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.36/10.58 apply (zenon_L44_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.36/10.58 apply (zenon_L771_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.36/10.58 apply (zenon_L595_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.36/10.58 apply (zenon_L384_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.36/10.58 apply (zenon_L93_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.36/10.58 apply (zenon_L60_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.58 apply (zenon_L772_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.58 apply (zenon_L77_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.58 apply (zenon_L774_); trivial. % 10.36/10.58 apply (zenon_L506_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.58 exact (zenon_H8c zenon_H91). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.58 apply (zenon_L193_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hcb ]. % 10.36/10.58 apply (zenon_L44_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hcb); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hcc ]. % 10.36/10.58 apply (zenon_L762_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hcc); [ zenon_intro zenon_H74 | zenon_intro zenon_Hc7 ]. % 10.36/10.58 apply (zenon_L595_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H152 | zenon_intro zenon_H15c ]. % 10.36/10.58 apply (zenon_L384_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H120 | zenon_intro zenon_H15d ]. % 10.36/10.58 apply (zenon_L766_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15d); [ zenon_intro zenon_Hfc | zenon_intro zenon_H159 ]. % 10.36/10.58 apply (zenon_L60_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.58 apply (zenon_L81_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.58 apply (zenon_L768_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.58 apply (zenon_L773_); trivial. % 10.36/10.58 apply (zenon_L506_); trivial. % 10.36/10.58 apply (zenon_L782_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_L771_); trivial. % 10.36/10.58 apply (zenon_L768_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L299_); trivial. % 10.36/10.58 apply (zenon_L385_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ]. % 10.36/10.58 apply (zenon_L775_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H91 | zenon_intro zenon_He4 ]. % 10.36/10.58 exact (zenon_H8c zenon_H91). % 10.36/10.58 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdd ]. % 10.36/10.58 apply (zenon_L307_); trivial. % 10.36/10.58 apply (zenon_L97_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.58 apply (zenon_L783_); trivial. % 10.36/10.58 exact (zenon_H59 zenon_H56). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.58 apply (zenon_L56_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.58 apply (zenon_L784_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.58 apply (zenon_L147_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.58 apply (zenon_L148_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.58 apply (zenon_L785_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.58 apply (zenon_L150_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.58 apply (zenon_L672_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.58 apply (zenon_L786_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.58 apply (zenon_L154_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.58 apply (zenon_L155_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.58 apply (zenon_L288_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.58 apply (zenon_L157_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.58 apply (zenon_L158_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.58 apply (zenon_L159_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.58 apply (zenon_L160_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.58 apply (zenon_L679_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.58 apply (zenon_L265_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.58 apply (zenon_L164_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.58 apply (zenon_L165_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.58 apply (zenon_L166_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1d8). zenon_intro zenon_H13b. zenon_intro zenon_H1d9. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1d9). zenon_intro zenon_H76. zenon_intro zenon_H24. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 apply (zenon_L787_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_L788_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.58 apply (zenon_L787_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.58 exact (zenon_H6e zenon_H6a). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_L755_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L48_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15e); [ zenon_intro zenon_H5a | zenon_intro zenon_H15f ]. % 10.36/10.58 apply (zenon_L383_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H119 | zenon_intro zenon_H160 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.58 apply (zenon_L755_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.58 exact (zenon_H8c zenon_H91). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.58 apply (zenon_L287_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H2d7 ]. % 10.36/10.58 apply (zenon_L762_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2d7); [ zenon_intro zenon_H101 | zenon_intro zenon_H2d8 ]. % 10.36/10.58 apply (zenon_L636_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2d8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H120 ]. % 10.36/10.58 apply (zenon_L333_); trivial. % 10.36/10.58 apply (zenon_L212_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H150 | zenon_intro zenon_H158 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.36/10.58 exact (zenon_H6e zenon_H6a). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.36/10.58 apply (zenon_L131_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H2ba ]. % 10.36/10.58 apply (zenon_L755_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H91 | zenon_intro zenon_H2bb ]. % 10.36/10.58 exact (zenon_H8c zenon_H91). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H252 ]. % 10.36/10.58 apply (zenon_L287_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H13c | zenon_intro zenon_H17f ]. % 10.36/10.58 apply (zenon_L790_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H180 ]. % 10.36/10.58 apply (zenon_L776_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H17a | zenon_intro zenon_H17c ]. % 10.36/10.58 apply (zenon_L308_); trivial. % 10.36/10.58 apply (zenon_L341_); trivial. % 10.36/10.58 apply (zenon_L103_); trivial. % 10.36/10.58 apply (zenon_L123_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_L755_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L48_); trivial. % 10.36/10.58 apply (zenon_L143_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.58 apply (zenon_L504_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.58 apply (zenon_L791_); trivial. % 10.36/10.58 apply (zenon_L756_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.58 apply (zenon_L710_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.58 apply (zenon_L169_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H127. zenon_intro zenon_H1e2. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H1e5. zenon_intro zenon_H2e. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H289); [ zenon_intro zenon_H5a | zenon_intro zenon_H28a ]. % 10.36/10.58 apply (zenon_L295_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28a); [ zenon_intro zenon_H13c | zenon_intro zenon_H28b ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 exact (zenon_H30 zenon_H2d). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.36/10.58 apply (zenon_L793_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.36/10.58 apply (zenon_L796_); trivial. % 10.36/10.58 apply (zenon_L187_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_L302_); trivial. % 10.36/10.58 apply (zenon_L77_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H28b); [ zenon_intro zenon_H152 | zenon_intro zenon_H13b ]. % 10.36/10.58 apply (zenon_L301_); trivial. % 10.36/10.58 apply (zenon_L170_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L48_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 exact (zenon_H30 zenon_H2d). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H24f ]. % 10.36/10.58 apply (zenon_L797_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H36 | zenon_intro zenon_H250 ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H101 | zenon_intro zenon_H175 ]. % 10.36/10.58 apply (zenon_L796_); trivial. % 10.36/10.58 apply (zenon_L187_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_L798_); trivial. % 10.36/10.58 apply (zenon_L77_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.58 exact (zenon_H30 zenon_H2d). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.58 apply (zenon_L824_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H46 | zenon_intro zenon_H1a6 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H1a7 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12d); [ zenon_intro zenon_H2d | zenon_intro zenon_H12e ]. % 10.36/10.58 exact (zenon_H30 zenon_H2d). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H6f | zenon_intro zenon_H12f ]. % 10.36/10.58 apply (zenon_L826_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12f); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H128 ]. % 10.36/10.58 apply (zenon_L302_); trivial. % 10.36/10.58 apply (zenon_L77_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_Hcd | zenon_intro zenon_He5 ]. % 10.36/10.58 apply (zenon_L48_); trivial. % 10.36/10.58 apply (zenon_L663_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.58 apply (zenon_L172_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.58 apply (zenon_L484_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.58 apply (zenon_L174_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.58 apply (zenon_L827_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.58 apply (zenon_L828_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.58 apply (zenon_L178_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.58 apply (zenon_L179_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.58 apply (zenon_L180_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.58 apply (zenon_L181_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.58 apply (zenon_L182_); trivial. % 10.36/10.58 apply (zenon_L183_); trivial. % 10.36/10.58 apply (zenon_L841_); trivial. % 10.36/10.58 apply (zenon_L851_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H396); [ zenon_intro zenon_H8c | zenon_intro zenon_H8b ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1ed ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.58 apply (zenon_L1_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.58 apply (zenon_L2_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.58 apply (zenon_L3_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.58 apply (zenon_L4_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.58 apply (zenon_L5_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.58 apply (zenon_L6_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.58 apply (zenon_L744_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.58 apply (zenon_L799_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.58 apply (zenon_L10_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.58 apply (zenon_L750_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.58 apply (zenon_L13_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.58 apply (zenon_L751_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.58 apply (zenon_L15_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.58 apply (zenon_L802_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.58 apply (zenon_L803_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.58 apply (zenon_L19_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.58 apply (zenon_L20_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.58 apply (zenon_L21_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.58 apply (zenon_L757_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H6a. zenon_intro zenon_H77. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H6b. zenon_intro zenon_H2a. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H79. zenon_intro zenon_H78. % 10.36/10.58 apply (zenon_L859_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.58 apply (zenon_L24_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.58 apply (zenon_L25_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.58 apply (zenon_L26_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.58 apply (zenon_L27_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.58 apply (zenon_L805_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.58 apply (zenon_L31_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.58 apply (zenon_L32_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.58 apply (zenon_L760_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.58 apply (zenon_L783_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.58 apply (zenon_L56_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.58 apply (zenon_L784_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.58 apply (zenon_L147_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.58 apply (zenon_L148_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.58 apply (zenon_L785_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.58 apply (zenon_L150_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.58 apply (zenon_L672_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.58 apply (zenon_L786_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.58 apply (zenon_L154_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.58 apply (zenon_L155_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.58 apply (zenon_L288_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.58 apply (zenon_L157_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.58 apply (zenon_L158_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.58 apply (zenon_L159_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.58 apply (zenon_L160_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.58 apply (zenon_L679_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.58 apply (zenon_L265_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.58 apply (zenon_L164_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.58 apply (zenon_L165_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.58 apply (zenon_L166_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1d8). zenon_intro zenon_H13b. zenon_intro zenon_H1d9. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1d9). zenon_intro zenon_H76. zenon_intro zenon_H24. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.36/10.58 apply (zenon_L791_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.58 apply (zenon_L811_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.58 apply (zenon_L169_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H127. zenon_intro zenon_H1e2. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H1e5. zenon_intro zenon_H2e. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.36/10.58 apply (zenon_L824_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.58 apply (zenon_L172_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.58 apply (zenon_L484_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.58 apply (zenon_L174_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.58 apply (zenon_L814_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.58 apply (zenon_L828_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.58 apply (zenon_L178_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.58 apply (zenon_L179_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.58 apply (zenon_L180_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.58 apply (zenon_L181_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.58 apply (zenon_L182_); trivial. % 10.36/10.58 apply (zenon_L183_); trivial. % 10.36/10.58 apply (zenon_L853_); trivial. % 10.36/10.58 apply (zenon_L817_); trivial. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H390). zenon_intro zenon_H67. zenon_intro zenon_H398. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H398). zenon_intro zenon_H39a. zenon_intro zenon_H399. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H399). zenon_intro zenon_H39c. zenon_intro zenon_H39b. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H39b). zenon_intro zenon_H320. zenon_intro zenon_H39d. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H39a); [ zenon_intro zenon_H58 | zenon_intro zenon_H56 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H39c); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Hef ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_Hff | zenon_intro zenon_Hd4 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.58 apply (zenon_L1_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.58 apply (zenon_L2_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.58 apply (zenon_L3_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.58 apply (zenon_L4_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.58 apply (zenon_L5_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.58 apply (zenon_L6_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H2d. zenon_intro zenon_H3d. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H2f. zenon_intro zenon_H80. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H103. zenon_intro zenon_H1bd. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hb9 | zenon_intro zenon_He2 ]. % 10.36/10.58 apply (zenon_L860_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He3 ]. % 10.36/10.58 exact (zenon_H1bd zenon_Hc3). % 10.36/10.58 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd4 ]. % 10.36/10.58 apply (zenon_L328_); trivial. % 10.36/10.58 apply (zenon_L864_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.58 apply (zenon_L865_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.58 apply (zenon_L10_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H42. zenon_intro zenon_H4c. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H44. zenon_intro zenon_H8f. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 apply (zenon_L869_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_L870_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_L421_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H191); [ zenon_intro zenon_H31 | zenon_intro zenon_H192 ]. % 10.36/10.58 apply (zenon_L869_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H192); [ zenon_intro zenon_H6a | zenon_intro zenon_H193 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_L197_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L867_); trivial. % 10.36/10.58 apply (zenon_L871_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_Hfa | zenon_intro zenon_H133 ]. % 10.36/10.58 apply (zenon_L906_); trivial. % 10.36/10.58 apply (zenon_L907_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.58 apply (zenon_L13_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.58 apply (zenon_L607_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.58 apply (zenon_L15_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.58 apply (zenon_L908_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.58 apply (zenon_L874_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.58 apply (zenon_L875_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.58 apply (zenon_L20_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.58 apply (zenon_L21_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.58 apply (zenon_L922_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.58 apply (zenon_L857_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.58 apply (zenon_L24_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.58 apply (zenon_L25_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.58 apply (zenon_L26_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.58 apply (zenon_L27_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.58 apply (zenon_L931_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.58 apply (zenon_L31_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.58 apply (zenon_L32_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.58 apply (zenon_L357_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.58 apply (zenon_L878_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.58 apply (zenon_L56_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.58 apply (zenon_L879_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.58 apply (zenon_L880_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.58 apply (zenon_L148_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_Hb9. zenon_intro zenon_H1ad. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1ad). zenon_intro zenon_H71. zenon_intro zenon_H24. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H31 | zenon_intro zenon_H1a4 ]. % 10.36/10.58 apply (zenon_L350_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H1a5 ]. % 10.36/10.58 apply (zenon_L882_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H16e | zenon_intro zenon_H198 ]. % 10.36/10.58 apply (zenon_L883_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H6a | zenon_intro zenon_H2ac ]. % 10.36/10.58 exact (zenon_H6e zenon_H6a). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H36 | zenon_intro zenon_H2ad ]. % 10.36/10.58 apply (zenon_L312_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H8b | zenon_intro zenon_Hef ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H74 | zenon_intro zenon_H291 ]. % 10.36/10.58 exact (zenon_H71 zenon_H74). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H103 | zenon_intro zenon_H292 ]. % 10.36/10.58 apply (zenon_L122_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfc ]. % 10.36/10.58 apply (zenon_L299_); trivial. % 10.36/10.58 exact (zenon_Hff zenon_Hfc). % 10.36/10.58 apply (zenon_L191_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.58 apply (zenon_L504_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.58 apply (zenon_L867_); trivial. % 10.36/10.58 apply (zenon_L884_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.58 apply (zenon_L150_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.58 apply (zenon_L692_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1b7). zenon_intro zenon_Hc3. zenon_intro zenon_H1b8. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H163. zenon_intro zenon_H2e. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H308); [ zenon_intro zenon_H1f | zenon_intro zenon_H309 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H119 | zenon_intro zenon_H12b ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H131 | zenon_intro zenon_H246 ]. % 10.36/10.58 apply (zenon_L81_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H128 | zenon_intro zenon_H247 ]. % 10.36/10.58 apply (zenon_L222_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H241 | zenon_intro zenon_H79 ]. % 10.36/10.58 apply (zenon_L932_); trivial. % 10.36/10.58 apply (zenon_L548_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12b); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H12c ]. % 10.36/10.58 exact (zenon_Ha3 zenon_Ha2). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H12c); [ zenon_intro zenon_H120 | zenon_intro zenon_H127 ]. % 10.36/10.58 apply (zenon_L73_); trivial. % 10.36/10.58 apply (zenon_L881_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H309); [ zenon_intro zenon_H2d | zenon_intro zenon_H30a ]. % 10.36/10.58 exact (zenon_H30 zenon_H2d). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H30a); [ zenon_intro zenon_H42 | zenon_intro zenon_H56 ]. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H74 | zenon_intro zenon_H291 ]. % 10.36/10.58 apply (zenon_L677_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H103 | zenon_intro zenon_H292 ]. % 10.36/10.58 exact (zenon_H163 zenon_H103). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H51 | zenon_intro zenon_Hfc ]. % 10.36/10.58 apply (zenon_L287_); trivial. % 10.36/10.58 exact (zenon_Hff zenon_Hfc). % 10.36/10.58 apply (zenon_L928_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.58 apply (zenon_L154_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.58 apply (zenon_L155_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.58 apply (zenon_L885_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.58 apply (zenon_L157_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.58 apply (zenon_L158_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.58 apply (zenon_L159_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.58 apply (zenon_L160_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.58 apply (zenon_L886_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.58 apply (zenon_L929_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.58 apply (zenon_L164_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.58 apply (zenon_L888_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.58 apply (zenon_L166_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.58 apply (zenon_L889_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.58 apply (zenon_L890_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.58 apply (zenon_L169_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.58 apply (zenon_L891_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.58 apply (zenon_L172_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.58 apply (zenon_L892_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.58 apply (zenon_L174_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.58 apply (zenon_L523_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.58 apply (zenon_L388_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.58 apply (zenon_L178_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.58 apply (zenon_L179_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.58 apply (zenon_L893_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.58 apply (zenon_L894_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.58 apply (zenon_L895_); trivial. % 10.36/10.58 apply (zenon_L896_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H1d | zenon_intro zenon_H203 ]. % 10.36/10.58 apply (zenon_L1_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H22 | zenon_intro zenon_H204 ]. % 10.36/10.58 apply (zenon_L2_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H25 | zenon_intro zenon_H205 ]. % 10.36/10.58 apply (zenon_L3_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H205); [ zenon_intro zenon_H28 | zenon_intro zenon_H206 ]. % 10.36/10.58 apply (zenon_L4_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H206); [ zenon_intro zenon_H2b | zenon_intro zenon_H207 ]. % 10.36/10.58 apply (zenon_L5_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H207); [ zenon_intro zenon_H32 | zenon_intro zenon_H208 ]. % 10.36/10.58 apply (zenon_L6_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H208); [ zenon_intro zenon_H3c | zenon_intro zenon_H209 ]. % 10.36/10.58 apply (zenon_L864_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H209); [ zenon_intro zenon_H3e | zenon_intro zenon_H20a ]. % 10.36/10.58 apply (zenon_L865_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20a); [ zenon_intro zenon_H40 | zenon_intro zenon_H20b ]. % 10.36/10.58 apply (zenon_L10_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H4b | zenon_intro zenon_H20c ]. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H42. zenon_intro zenon_H4c. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H44. zenon_intro zenon_H8f. % 10.36/10.58 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H281); [ zenon_intro zenon_H46 | zenon_intro zenon_H282 ]. % 10.36/10.58 exact (zenon_H44 zenon_H46). % 10.36/10.58 apply (zenon_or_s _ _ zenon_H282); [ zenon_intro zenon_Hba | zenon_intro zenon_H283 ]. % 10.36/10.58 apply (zenon_L197_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H283); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H136 ]. % 10.36/10.58 apply (zenon_L162_); trivial. % 10.36/10.58 apply (zenon_L905_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20c); [ zenon_intro zenon_H4d | zenon_intro zenon_H20d ]. % 10.36/10.58 apply (zenon_L13_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H52 | zenon_intro zenon_H20e ]. % 10.36/10.58 apply (zenon_L607_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H54 | zenon_intro zenon_H20f ]. % 10.36/10.58 apply (zenon_L15_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H20f); [ zenon_intro zenon_H5f | zenon_intro zenon_H210 ]. % 10.36/10.58 apply (zenon_L908_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H61 | zenon_intro zenon_H211 ]. % 10.36/10.58 apply (zenon_L900_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H63 | zenon_intro zenon_H212 ]. % 10.36/10.58 apply (zenon_L875_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H68 | zenon_intro zenon_H213 ]. % 10.36/10.58 apply (zenon_L20_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H6c | zenon_intro zenon_H214 ]. % 10.36/10.58 apply (zenon_L21_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H70 | zenon_intro zenon_H215 ]. % 10.36/10.58 apply (zenon_L922_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H75 | zenon_intro zenon_H216 ]. % 10.36/10.58 apply (zenon_L857_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H7a | zenon_intro zenon_H217 ]. % 10.36/10.58 apply (zenon_L24_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H7c | zenon_intro zenon_H218 ]. % 10.36/10.58 apply (zenon_L25_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H7e | zenon_intro zenon_H219 ]. % 10.36/10.58 apply (zenon_L26_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H81 | zenon_intro zenon_H21a ]. % 10.36/10.58 apply (zenon_L27_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H89 | zenon_intro zenon_H21b ]. % 10.36/10.58 apply (zenon_L931_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21b); [ zenon_intro zenon_H8d | zenon_intro zenon_H21c ]. % 10.36/10.58 apply (zenon_L31_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_H92 | zenon_intro zenon_H21d ]. % 10.36/10.58 apply (zenon_L32_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21d); [ zenon_intro zenon_H18f | zenon_intro zenon_H21e ]. % 10.36/10.58 apply (zenon_L357_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_Hed | zenon_intro zenon_H21f ]. % 10.36/10.58 apply (zenon_L878_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_Hf0 | zenon_intro zenon_H220 ]. % 10.36/10.58 apply (zenon_L56_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H16f | zenon_intro zenon_H221 ]. % 10.36/10.58 apply (zenon_L901_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H222 ]. % 10.36/10.58 apply (zenon_L880_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1aa | zenon_intro zenon_H223 ]. % 10.36/10.58 apply (zenon_L148_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H1ac | zenon_intro zenon_H224 ]. % 10.36/10.58 apply (zenon_L902_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H1ae | zenon_intro zenon_H225 ]. % 10.36/10.58 apply (zenon_L150_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H226 ]. % 10.36/10.58 apply (zenon_L692_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H226); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H227 ]. % 10.36/10.58 apply (zenon_L903_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H227); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H228 ]. % 10.36/10.58 apply (zenon_L154_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H228); [ zenon_intro zenon_H1bb | zenon_intro zenon_H229 ]. % 10.36/10.58 apply (zenon_L155_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H229); [ zenon_intro zenon_H1be | zenon_intro zenon_H22a ]. % 10.36/10.58 apply (zenon_L885_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H22b ]. % 10.36/10.58 apply (zenon_L157_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H1c2 | zenon_intro zenon_H22c ]. % 10.36/10.58 apply (zenon_L158_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H22d ]. % 10.36/10.58 apply (zenon_L159_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H22e ]. % 10.36/10.58 apply (zenon_L160_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H22f ]. % 10.36/10.58 apply (zenon_L886_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1cf | zenon_intro zenon_H230 ]. % 10.36/10.58 apply (zenon_L929_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H231 ]. % 10.36/10.58 apply (zenon_L164_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H232 ]. % 10.36/10.58 apply (zenon_L888_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H233 ]. % 10.36/10.58 apply (zenon_L166_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H234 ]. % 10.36/10.58 apply (zenon_L889_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H1da | zenon_intro zenon_H235 ]. % 10.36/10.58 apply (zenon_L890_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1dc | zenon_intro zenon_H236 ]. % 10.36/10.58 apply (zenon_L169_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H237 ]. % 10.36/10.58 apply (zenon_L891_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H238 ]. % 10.36/10.58 apply (zenon_L172_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1e6 | zenon_intro zenon_H239 ]. % 10.36/10.58 apply (zenon_L892_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H23a ]. % 10.36/10.58 apply (zenon_L174_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_H1eb | zenon_intro zenon_H23b ]. % 10.36/10.58 apply (zenon_L523_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23b); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H23c ]. % 10.36/10.58 apply (zenon_L388_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23c); [ zenon_intro zenon_H1f5 | zenon_intro zenon_H23d ]. % 10.36/10.58 apply (zenon_L178_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23d); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H23e ]. % 10.36/10.58 apply (zenon_L179_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23e); [ zenon_intro zenon_H1fa | zenon_intro zenon_H23f ]. % 10.36/10.58 apply (zenon_L893_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H23f); [ zenon_intro zenon_H1fc | zenon_intro zenon_H240 ]. % 10.36/10.58 apply (zenon_L894_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H240); [ zenon_intro zenon_H1fe | zenon_intro zenon_H200 ]. % 10.36/10.58 apply (zenon_L895_); trivial. % 10.36/10.58 apply (zenon_L896_); trivial. % 10.36/10.58 apply (zenon_L904_); trivial. % 10.36/10.58 apply (zenon_or_s _ _ zenon_H39c); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Hef ]. % 10.36/10.58 apply (zenon_L930_); trivial. % 10.36/10.58 apply (zenon_L918_); trivial. % 10.36/10.58 Qed. % 10.36/10.58 % SZS output end Proof % 10.36/10.58 (* END-PROOF *) % 10.36/10.58 nodes searched: 216071 % 10.36/10.58 max branch formulas: 347 % 10.36/10.58 proof nodes created: 9660 % 10.36/10.58 formulas created: 65493 % 10.36/10.58 %------------------------------------------------------------------------------