%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG146+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n026.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 18:30:23 EDT 2022 % Result : Unsatisfiable 5.56s 5.74s % Output : Proof 5.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : ALG146+1 : TPTP v8.1.0. Released v2.7.0. % 0.10/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n026.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jun 8 00:46:46 EDT 2022 % 0.12/0.33 % CPUTime : % 5.56/5.74 (* PROOF-FOUND *) % 5.56/5.74 % SZS status Unsatisfiable % 5.56/5.74 (* BEGIN-PROOF *) % 5.56/5.74 % SZS output start Proof % 5.56/5.74 Theorem zenon_thm : False. % 5.56/5.74 Proof. % 5.56/5.74 assert (zenon_L1_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H1d. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H1f. zenon_intro zenon_H20. % 5.56/5.74 exact (zenon_H20 zenon_H1f). % 5.56/5.74 (* end of lemma zenon_L1_ *) % 5.56/5.74 assert (zenon_L2_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H21 zenon_H22 zenon_H23 zenon_H24 zenon_H25 zenon_H26. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 5.56/5.74 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H23. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H22. % 5.56/5.74 cut (((e0) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 5.56/5.74 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H2a. apply refl_equal. % 5.56/5.74 apply zenon_H29. apply sym_equal. exact zenon_H28. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 5.56/5.74 exact (zenon_H24 zenon_H2c). % 5.56/5.74 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 5.56/5.74 exact (zenon_H25 zenon_H2e). % 5.56/5.74 exact (zenon_H26 zenon_H2d). % 5.56/5.74 (* end of lemma zenon_L2_ *) % 5.56/5.74 assert (zenon_L3_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H2f zenon_H21 zenon_H23 zenon_H25 zenon_H26. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H31. zenon_intro zenon_H24. % 5.56/5.74 apply (zenon_L2_); trivial. % 5.56/5.74 (* end of lemma zenon_L3_ *) % 5.56/5.74 assert (zenon_L4_ : (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H32 zenon_H1f zenon_H33. % 5.56/5.74 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e2)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H32. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H1f. % 5.56/5.74 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 5.56/5.74 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H35. apply refl_equal. % 5.56/5.74 apply zenon_H34. apply sym_equal. exact zenon_H33. % 5.56/5.74 (* end of lemma zenon_L4_ *) % 5.56/5.74 assert (zenon_L5_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H36 zenon_H32 zenon_H1f. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.56/5.74 apply (zenon_L4_); trivial. % 5.56/5.74 (* end of lemma zenon_L5_ *) % 5.56/5.74 assert (zenon_L6_ : (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H38 zenon_H1f zenon_H39. % 5.56/5.74 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e3) (e0)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H38. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H1f. % 5.56/5.74 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 5.56/5.74 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H35. apply refl_equal. % 5.56/5.74 apply zenon_H3a. apply sym_equal. exact zenon_H39. % 5.56/5.74 (* end of lemma zenon_L6_ *) % 5.56/5.74 assert (zenon_L7_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e0)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H3b zenon_H38 zenon_H1f. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.56/5.74 apply (zenon_L6_); trivial. % 5.56/5.74 (* end of lemma zenon_L7_ *) % 5.56/5.74 assert (zenon_L8_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H3f zenon_H1f. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.74 exact (zenon_H20 zenon_H1f). % 5.56/5.74 (* end of lemma zenon_L8_ *) % 5.56/5.74 assert (zenon_L9_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H43. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H2c. zenon_intro zenon_H44. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H2c. zenon_intro zenon_H24. % 5.56/5.74 exact (zenon_H24 zenon_H2c). % 5.56/5.74 (* end of lemma zenon_L9_ *) % 5.56/5.74 assert (zenon_L10_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H45 zenon_H46 zenon_H47. % 5.56/5.74 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H45. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H46. % 5.56/5.74 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 5.56/5.74 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H49. apply refl_equal. % 5.56/5.74 apply zenon_H48. apply sym_equal. exact zenon_H47. % 5.56/5.74 (* end of lemma zenon_L10_ *) % 5.56/5.74 assert (zenon_L11_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H4a zenon_H4b zenon_H46 zenon_H45 zenon_H4c zenon_H4d. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 5.56/5.74 exact (zenon_H4b zenon_H4f). % 5.56/5.74 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H47 | zenon_intro zenon_H50 ]. % 5.56/5.74 apply (zenon_L10_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 5.56/5.74 exact (zenon_H4c zenon_H52). % 5.56/5.74 exact (zenon_H4d zenon_H51). % 5.56/5.74 (* end of lemma zenon_L11_ *) % 5.56/5.74 assert (zenon_L12_ : (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H53 zenon_H1f zenon_H3d. % 5.56/5.74 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H53. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H1f. % 5.56/5.74 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 5.56/5.74 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H35. apply refl_equal. % 5.56/5.74 apply zenon_H54. apply sym_equal. exact zenon_H3d. % 5.56/5.74 (* end of lemma zenon_L12_ *) % 5.56/5.74 assert (zenon_L13_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e1) (e3)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H55 zenon_H56 zenon_H57 zenon_H58 zenon_H59 zenon_H3e. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 5.56/5.74 cut (((op (e1) (e3)) = (e0)) = ((op (e1) (e3)) = (op (e3) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H57. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H56. % 5.56/5.74 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 5.56/5.74 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H5d. apply refl_equal. % 5.56/5.74 apply zenon_H5c. apply sym_equal. exact zenon_H5b. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 5.56/5.74 exact (zenon_H58 zenon_H5f). % 5.56/5.74 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 5.56/5.74 exact (zenon_H59 zenon_H61). % 5.56/5.74 exact (zenon_H3e zenon_H60). % 5.56/5.74 (* end of lemma zenon_L13_ *) % 5.56/5.74 assert (zenon_L14_ : (~((e2) = (e2))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H62. % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L14_ *) % 5.56/5.74 assert (zenon_L15_ : (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H63 zenon_H64 zenon_H65. % 5.56/5.74 cut (((op (e2) (e3)) = (e2)) = ((e0) = (e2))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H63. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H64. % 5.56/5.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.74 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_H66 zenon_H65). % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L15_ *) % 5.56/5.74 assert (zenon_L16_ : (((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0))))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H1d. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H1f. zenon_intro zenon_H20. % 5.56/5.74 exact (zenon_H20 zenon_H1f). % 5.56/5.74 (* end of lemma zenon_L16_ *) % 5.56/5.74 assert (zenon_L17_ : (~((e0) = (e0))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H67. % 5.56/5.74 apply zenon_H67. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L17_ *) % 5.56/5.74 assert (zenon_L18_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H31 zenon_H68 zenon_H63. % 5.56/5.74 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.56/5.74 cut (((e2) = (e2)) = ((e0) = (e2))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H63. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H69. % 5.56/5.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.74 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e1) (e0)) = (e0)) = ((e2) = (e0))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H6a. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H31. % 5.56/5.74 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.74 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_H6b zenon_H68). % 5.56/5.74 apply zenon_H67. apply refl_equal. % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L18_ *) % 5.56/5.74 assert (zenon_L19_ : ((op (e1) (e0)) = (e0)) -> ((op (e1) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H31 zenon_H6c zenon_H6d. % 5.56/5.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.74 cut (((e3) = (e3)) = ((e0) = (e3))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H6d. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H6e. % 5.56/5.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.74 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e1) (e0)) = (e0)) = ((e3) = (e0))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H70. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H31. % 5.56/5.74 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.74 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_H71 zenon_H6c). % 5.56/5.74 apply zenon_H67. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L19_ *) % 5.56/5.74 assert (zenon_L20_ : (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e2)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H72 zenon_H22 zenon_H33. % 5.56/5.74 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e2)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H72. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H22. % 5.56/5.74 cut (((e0) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 5.56/5.74 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H2a. apply refl_equal. % 5.56/5.74 apply zenon_H34. apply sym_equal. exact zenon_H33. % 5.56/5.74 (* end of lemma zenon_L20_ *) % 5.56/5.74 assert (zenon_L21_ : (~((e0) = (e2))) -> ((op (e1) (e2)) = (e2)) -> ((op (e1) (e2)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H63 zenon_H73 zenon_H74. % 5.56/5.74 cut (((op (e1) (e2)) = (e2)) = ((e0) = (e2))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H63. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H73. % 5.56/5.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.74 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_H75 zenon_H74). % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L21_ *) % 5.56/5.74 assert (zenon_L22_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))) -> ((op (e2) (e2)) = (e1)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H76 zenon_H47. % 5.56/5.74 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H77]. % 5.56/5.74 cut (((op (e2) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H77]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_H77 zenon_H47). % 5.56/5.74 exact (zenon_H77 zenon_H47). % 5.56/5.74 (* end of lemma zenon_L22_ *) % 5.56/5.74 assert (zenon_L23_ : (~((e3) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H6f. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L23_ *) % 5.56/5.74 assert (zenon_L24_ : ((op (e3) (e2)) = (e0)) -> ((op (e1) (e1)) = (e3)) -> ((op (e2) (e2)) = (e1)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H78 zenon_H2d zenon_H47. % 5.56/5.74 apply (zenon_notand_s _ _ ax16); [ zenon_intro zenon_H48 | zenon_intro zenon_H79 ]. % 5.56/5.74 apply zenon_H48. apply sym_equal. exact zenon_H47. % 5.56/5.74 apply (zenon_notand_s _ _ zenon_H79); [ zenon_intro zenon_H7b | zenon_intro zenon_H7a ]. % 5.56/5.74 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.56/5.74 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e3) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H7b. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H7c. % 5.56/5.74 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.56/5.74 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e1) (e1)) = (e3)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e3))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H7e. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H2d. % 5.56/5.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.74 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 5.56/5.74 congruence. % 5.56/5.74 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.56/5.74 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H7f. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H7c. % 5.56/5.74 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.56/5.74 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 5.56/5.74 congruence. % 5.56/5.74 apply (zenon_L22_); trivial. % 5.56/5.74 apply zenon_H7d. apply refl_equal. % 5.56/5.74 apply zenon_H7d. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 apply zenon_H7d. apply refl_equal. % 5.56/5.74 apply zenon_H7d. apply refl_equal. % 5.56/5.74 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H80 | zenon_intro zenon_H81 ]. % 5.56/5.74 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2))) = ((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H7a. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H80. % 5.56/5.74 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 5.56/5.74 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e3) (e2)) = (e0)) = ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (e0))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H82. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H78. % 5.56/5.74 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.74 cut (((op (e3) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 5.56/5.74 congruence. % 5.56/5.74 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H80 | zenon_intro zenon_H81 ]. % 5.56/5.74 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2))) = ((op (e3) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H83. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H80. % 5.56/5.74 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 5.56/5.74 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.74 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e1) (e1)) = (e3)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e3))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H7e. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H2d. % 5.56/5.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.74 cut (((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 5.56/5.74 congruence. % 5.56/5.74 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.56/5.74 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e1) (e1)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H7f. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H7c. % 5.56/5.74 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.56/5.74 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 5.56/5.74 congruence. % 5.56/5.74 apply (zenon_L22_); trivial. % 5.56/5.74 apply zenon_H7d. apply refl_equal. % 5.56/5.74 apply zenon_H7d. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 apply zenon_H81. apply refl_equal. % 5.56/5.74 apply zenon_H81. apply refl_equal. % 5.56/5.74 apply zenon_H67. apply refl_equal. % 5.56/5.74 apply zenon_H81. apply refl_equal. % 5.56/5.74 apply zenon_H81. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L24_ *) % 5.56/5.74 assert (zenon_L25_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> ((op (e1) (e1)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H4a zenon_H4b zenon_H2d zenon_H78 zenon_H4c zenon_H4d. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 5.56/5.74 exact (zenon_H4b zenon_H4f). % 5.56/5.74 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H47 | zenon_intro zenon_H50 ]. % 5.56/5.74 apply (zenon_L24_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 5.56/5.74 exact (zenon_H4c zenon_H52). % 5.56/5.74 exact (zenon_H4d zenon_H51). % 5.56/5.74 (* end of lemma zenon_L25_ *) % 5.56/5.74 assert (zenon_L26_ : ((op (e1) (e2)) = (e2)) -> ((op (e1) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H73 zenon_H85 zenon_H86. % 5.56/5.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.74 cut (((e3) = (e3)) = ((e2) = (e3))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H86. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H6e. % 5.56/5.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.74 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e1) (e2)) = (e2)) = ((e3) = (e2))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H87. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H73. % 5.56/5.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.74 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_H88 zenon_H85). % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L26_ *) % 5.56/5.74 assert (zenon_L27_ : ((op (e3) (e3)) = (e3)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H60 zenon_H89 zenon_H57. % 5.56/5.74 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e1) (e3)) = (op (e3) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H57. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H8a. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e1) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H8c. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H60. % 5.56/5.74 cut (((e3) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 apply zenon_H8d. apply sym_equal. exact zenon_H89. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L27_ *) % 5.56/5.74 assert (zenon_L28_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H8e zenon_H6d zenon_H31 zenon_H4d zenon_H4c zenon_H4b zenon_H4a zenon_H63 zenon_H72 zenon_H22 zenon_H8f zenon_H86 zenon_H73 zenon_H60 zenon_H57. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.56/5.74 apply (zenon_L19_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H33 | zenon_intro zenon_H92 ]. % 5.56/5.74 apply (zenon_L20_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H74 | zenon_intro zenon_H93 ]. % 5.56/5.74 apply (zenon_L21_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H4f | zenon_intro zenon_H78 ]. % 5.56/5.74 exact (zenon_H4b zenon_H4f). % 5.56/5.74 apply (zenon_L25_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.56/5.74 apply (zenon_L26_); trivial. % 5.56/5.74 apply (zenon_L27_); trivial. % 5.56/5.74 (* end of lemma zenon_L28_ *) % 5.56/5.74 assert (zenon_L29_ : (~((e1) = (e1))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H94. % 5.56/5.74 apply zenon_H94. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L29_ *) % 5.56/5.74 assert (zenon_L30_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H95 zenon_H96 zenon_H97. % 5.56/5.74 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.56/5.74 cut (((e2) = (e2)) = ((e1) = (e2))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H97. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H69. % 5.56/5.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.74 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e1) (e3)) = (e1)) = ((e2) = (e1))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H98. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H95. % 5.56/5.74 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.74 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_H99 zenon_H96). % 5.56/5.74 apply zenon_H94. apply refl_equal. % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L30_ *) % 5.56/5.74 assert (zenon_L31_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H36 zenon_H72 zenon_H22. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.56/5.74 apply (zenon_L20_); trivial. % 5.56/5.74 (* end of lemma zenon_L31_ *) % 5.56/5.74 assert (zenon_L32_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H3b zenon_H60. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.56/5.74 exact (zenon_H3e zenon_H60). % 5.56/5.74 (* end of lemma zenon_L32_ *) % 5.56/5.74 assert (zenon_L33_ : (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H9a zenon_H41 zenon_H95. % 5.56/5.74 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H9a. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H41. % 5.56/5.74 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 5.56/5.74 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H9c. apply refl_equal. % 5.56/5.74 apply zenon_H9b. apply sym_equal. exact zenon_H95. % 5.56/5.74 (* end of lemma zenon_L33_ *) % 5.56/5.74 assert (zenon_L34_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H3f zenon_H9a zenon_H95. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.74 apply (zenon_L33_); trivial. % 5.56/5.74 (* end of lemma zenon_L34_ *) % 5.56/5.74 assert (zenon_L35_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H46 zenon_H85 zenon_H9d. % 5.56/5.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.74 cut (((e3) = (e3)) = ((e1) = (e3))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H9d. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H6e. % 5.56/5.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.74 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e1) (e2)) = (e1)) = ((e3) = (e1))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H9e. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H46. % 5.56/5.74 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.74 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_H88 zenon_H85). % 5.56/5.74 apply zenon_H94. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L35_ *) % 5.56/5.74 assert (zenon_L36_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H8e zenon_H6d zenon_H31 zenon_H26 zenon_H9d zenon_H46 zenon_H60 zenon_H57. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.56/5.74 apply (zenon_L19_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.56/5.74 exact (zenon_H26 zenon_H2d). % 5.56/5.74 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.56/5.74 apply (zenon_L35_); trivial. % 5.56/5.74 apply (zenon_L27_); trivial. % 5.56/5.74 (* end of lemma zenon_L36_ *) % 5.56/5.74 assert (zenon_L37_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H2f zenon_H8e zenon_H6d zenon_H26 zenon_H9d zenon_H46 zenon_H60 zenon_H57. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H31. zenon_intro zenon_H24. % 5.56/5.74 apply (zenon_L36_); trivial. % 5.56/5.74 (* end of lemma zenon_L37_ *) % 5.56/5.74 assert (zenon_L38_ : (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H9f zenon_H41 zenon_H46. % 5.56/5.74 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e2)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H9f. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H41. % 5.56/5.74 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 5.56/5.74 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H9c. apply refl_equal. % 5.56/5.74 apply zenon_Ha0. apply sym_equal. exact zenon_H46. % 5.56/5.74 (* end of lemma zenon_L38_ *) % 5.56/5.74 assert (zenon_L39_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H3f zenon_H9f zenon_H46. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.74 apply (zenon_L38_); trivial. % 5.56/5.74 (* end of lemma zenon_L39_ *) % 5.56/5.74 assert (zenon_L40_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H22 zenon_Ha1 zenon_H6d. % 5.56/5.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.74 cut (((e3) = (e3)) = ((e0) = (e3))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H6d. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H6e. % 5.56/5.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.74 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e0) (e1)) = (e0)) = ((e3) = (e0))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H70. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H22. % 5.56/5.74 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.74 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_Ha2 zenon_Ha1). % 5.56/5.74 apply zenon_H67. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L40_ *) % 5.56/5.74 assert (zenon_L41_ : ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Ha3 zenon_Ha4 zenon_H9d. % 5.56/5.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.74 cut (((e3) = (e3)) = ((e1) = (e3))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H9d. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H6e. % 5.56/5.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.74 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e2) (e1)) = (e1)) = ((e3) = (e1))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H9e. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_Ha3. % 5.56/5.74 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.74 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_Ha5 zenon_Ha4). % 5.56/5.74 apply zenon_H94. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L41_ *) % 5.56/5.74 assert (zenon_L42_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H60 zenon_Ha6 zenon_Ha7. % 5.56/5.74 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e1)) = (op (e3) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Ha7. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H8a. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e1)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Ha8. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H60. % 5.56/5.74 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 apply zenon_Ha9. apply sym_equal. exact zenon_Ha6. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L42_ *) % 5.56/5.74 assert (zenon_L43_ : (((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))) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Haa zenon_H6d zenon_H22 zenon_H26 zenon_H9d zenon_Ha3 zenon_H60 zenon_Ha7. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hab ]. % 5.56/5.74 apply (zenon_L40_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H2d | zenon_intro zenon_Hac ]. % 5.56/5.74 exact (zenon_H26 zenon_H2d). % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha6 ]. % 5.56/5.74 apply (zenon_L41_); trivial. % 5.56/5.74 apply (zenon_L42_); trivial. % 5.56/5.74 (* end of lemma zenon_L43_ *) % 5.56/5.74 assert (zenon_L44_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Had zenon_H60. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.56/5.74 exact (zenon_H3e zenon_H60). % 5.56/5.74 (* end of lemma zenon_L44_ *) % 5.56/5.74 assert (zenon_L45_ : ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hb0 zenon_Hb1 zenon_H86. % 5.56/5.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.74 cut (((e3) = (e3)) = ((e2) = (e3))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H86. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H6e. % 5.56/5.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.74 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e0) (e2)) = (e2)) = ((e3) = (e2))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H87. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_Hb0. % 5.56/5.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.74 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_Hb2 zenon_Hb1). % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 apply zenon_H6f. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L45_ *) % 5.56/5.74 assert (zenon_L46_ : ((op (e3) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H60 zenon_Hb3 zenon_Hb4. % 5.56/5.74 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e0) (e3)) = (op (e3) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hb4. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H8a. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e0) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hb5. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H60. % 5.56/5.74 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 apply zenon_Hb6. apply sym_equal. exact zenon_Hb3. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L46_ *) % 5.56/5.74 assert (zenon_L47_ : (((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). % 5.56/5.74 do 0 intro. intros zenon_Hb7 zenon_Hb8 zenon_H6d zenon_H22 zenon_H86 zenon_Hb0 zenon_H60 zenon_Hb4. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.56/5.74 exact (zenon_Hb8 zenon_Hba). % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.56/5.74 apply (zenon_L40_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.56/5.74 apply (zenon_L45_); trivial. % 5.56/5.74 apply (zenon_L46_); trivial. % 5.56/5.74 (* end of lemma zenon_L47_ *) % 5.56/5.74 assert (zenon_L48_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (((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 (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hbc zenon_Hb7 zenon_Hb8 zenon_H6d zenon_H22 zenon_H86 zenon_H60 zenon_Hb4. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.56/5.74 apply (zenon_L47_); trivial. % 5.56/5.74 (* end of lemma zenon_L48_ *) % 5.56/5.74 assert (zenon_L49_ : ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e2)) -> (~((e1) = (e2))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H46 zenon_H73 zenon_H97. % 5.56/5.74 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.56/5.74 cut (((e2) = (e2)) = ((e1) = (e2))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H97. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H69. % 5.56/5.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.74 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e1) (e2)) = (e1)) = ((e2) = (e1))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H98. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H46. % 5.56/5.74 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.74 cut (((op (e1) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_Hbf zenon_H73). % 5.56/5.74 apply zenon_H94. apply refl_equal. % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 apply zenon_H62. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L49_ *) % 5.56/5.74 assert (zenon_L50_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1))))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e2))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hc0 zenon_H46 zenon_H97. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.56/5.74 apply (zenon_L49_); trivial. % 5.56/5.74 (* end of lemma zenon_L50_ *) % 5.56/5.74 assert (zenon_L51_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hc3. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_H52. zenon_intro zenon_Hc4. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_H52. zenon_intro zenon_H4c. % 5.56/5.74 exact (zenon_H4c zenon_H52). % 5.56/5.74 (* end of lemma zenon_L51_ *) % 5.56/5.74 assert (zenon_L52_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hc5 zenon_H60. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.56/5.74 exact (zenon_H3e zenon_H60). % 5.56/5.74 (* end of lemma zenon_L52_ *) % 5.56/5.74 assert (zenon_L53_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hc8 zenon_H60 zenon_Hb4. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.56/5.74 apply (zenon_L46_); trivial. % 5.56/5.74 (* end of lemma zenon_L53_ *) % 5.56/5.74 assert (zenon_L54_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hcb zenon_H60 zenon_H57. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.56/5.74 apply (zenon_L27_); trivial. % 5.56/5.74 (* end of lemma zenon_L54_ *) % 5.56/5.74 assert (zenon_L55_ : ((op (e3) (e3)) = (e3)) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H60 zenon_Hcd zenon_Hce. % 5.56/5.74 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e2) (e3)) = (op (e3) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hce. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H8a. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e2) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hcf. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H60. % 5.56/5.74 cut (((e3) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 apply zenon_Hd0. apply sym_equal. exact zenon_Hcd. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L55_ *) % 5.56/5.74 assert (zenon_L56_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hd1 zenon_H60 zenon_Hce. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.56/5.74 apply (zenon_L55_); trivial. % 5.56/5.74 (* end of lemma zenon_L56_ *) % 5.56/5.74 assert (zenon_L57_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hd4. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H60. zenon_intro zenon_Hd5. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H60. zenon_intro zenon_H3e. % 5.56/5.74 exact (zenon_H3e zenon_H60). % 5.56/5.74 (* end of lemma zenon_L57_ *) % 5.56/5.74 assert (zenon_L58_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.56/5.74 do 0 intro. intros zenon_H36 zenon_H52. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_Hd6. zenon_intro zenon_H4c. % 5.56/5.74 exact (zenon_H4c zenon_H52). % 5.56/5.74 (* end of lemma zenon_L58_ *) % 5.56/5.74 assert (zenon_L59_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hd7 zenon_H52. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.74 exact (zenon_H4c zenon_H52). % 5.56/5.74 (* end of lemma zenon_L59_ *) % 5.56/5.74 assert (zenon_L60_ : (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hd9 zenon_Hc2 zenon_H52. % 5.56/5.74 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e2)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hd9. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_Hc2. % 5.56/5.74 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 5.56/5.74 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_Hdb. apply refl_equal. % 5.56/5.74 apply zenon_Hda. apply sym_equal. exact zenon_H52. % 5.56/5.74 (* end of lemma zenon_L60_ *) % 5.56/5.74 assert (zenon_L61_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hc0 zenon_Hd9 zenon_H52. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.74 apply (zenon_L60_); trivial. % 5.56/5.74 (* end of lemma zenon_L61_ *) % 5.56/5.74 assert (zenon_L62_ : (((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2))))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hc3. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_H52. zenon_intro zenon_Hc4. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_H52. zenon_intro zenon_H4c. % 5.56/5.74 exact (zenon_H4c zenon_H52). % 5.56/5.74 (* end of lemma zenon_L62_ *) % 5.56/5.74 assert (zenon_L63_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hd1 zenon_H52. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.56/5.74 exact (zenon_H4c zenon_H52). % 5.56/5.74 (* end of lemma zenon_L63_ *) % 5.56/5.74 assert (zenon_L64_ : (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hdc zenon_H46 zenon_H95. % 5.56/5.74 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e1) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hdc. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H46. % 5.56/5.74 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 5.56/5.74 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H49. apply refl_equal. % 5.56/5.74 apply zenon_H9b. apply sym_equal. exact zenon_H95. % 5.56/5.74 (* end of lemma zenon_L64_ *) % 5.56/5.74 assert (zenon_L65_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_H97 zenon_Hb7 zenon_Hb4 zenon_H86 zenon_Hb8 zenon_Haa zenon_Ha7 zenon_H9f zenon_H72 zenon_H22 zenon_H8e zenon_H60 zenon_H57 zenon_H46 zenon_H9d zenon_H6d. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.74 apply (zenon_L16_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.74 apply (zenon_L37_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.74 apply (zenon_L31_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.74 apply (zenon_L32_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.74 apply (zenon_L39_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.74 apply (zenon_L9_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.74 apply (zenon_L43_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.74 apply (zenon_L44_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.74 apply (zenon_L48_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.74 apply (zenon_L50_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.74 apply (zenon_L51_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.74 apply (zenon_L52_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.74 apply (zenon_L53_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.74 apply (zenon_L54_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.74 apply (zenon_L56_); trivial. % 5.56/5.74 apply (zenon_L57_); trivial. % 5.56/5.74 apply (zenon_L64_); trivial. % 5.56/5.74 (* end of lemma zenon_L65_ *) % 5.56/5.74 assert (zenon_L66_ : (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hed zenon_H22 zenon_H3d. % 5.56/5.74 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e0) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hed. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H22. % 5.56/5.74 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 5.56/5.74 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H2a. apply refl_equal. % 5.56/5.74 apply zenon_H54. apply sym_equal. exact zenon_H3d. % 5.56/5.74 (* end of lemma zenon_L66_ *) % 5.56/5.74 assert (zenon_L67_ : (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hee zenon_H95 zenon_H56. % 5.56/5.74 cut (((op (e1) (e3)) = (e1)) = ((e0) = (e1))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hee. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H95. % 5.56/5.74 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.74 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 5.56/5.74 congruence. % 5.56/5.74 exact (zenon_Hef zenon_H56). % 5.56/5.74 apply zenon_H94. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L67_ *) % 5.56/5.74 assert (zenon_L68_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> ((op (e2) (e3)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hf0 zenon_Hd6 zenon_H65. % 5.56/5.74 cut (((op (e2) (e0)) = (e0)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hf0. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_Hd6. % 5.56/5.74 cut (((e0) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hf1]. % 5.56/5.74 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_Hf2. apply refl_equal. % 5.56/5.74 apply zenon_Hf1. apply sym_equal. exact zenon_H65. % 5.56/5.74 (* end of lemma zenon_L68_ *) % 5.56/5.74 assert (zenon_L69_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e2)) = (e0)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hf3 zenon_H39 zenon_H78. % 5.56/5.74 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hf3. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H39. % 5.56/5.74 cut (((e0) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 5.56/5.74 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_Hf5. apply refl_equal. % 5.56/5.74 apply zenon_Hf4. apply sym_equal. exact zenon_H78. % 5.56/5.74 (* end of lemma zenon_L69_ *) % 5.56/5.74 assert (zenon_L70_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_H57 zenon_H60 zenon_H86 zenon_H4a zenon_H4c zenon_H4d zenon_H6d zenon_H8e zenon_Hf7 zenon_Hf0 zenon_Hee zenon_H95 zenon_Hed zenon_Hf8 zenon_H8f zenon_H22 zenon_H72 zenon_H73 zenon_H63 zenon_H4b zenon_Hf3. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.56/5.74 exact (zenon_H20 zenon_H1f). % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.56/5.74 apply (zenon_L28_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H3d | zenon_intro zenon_Hfb ]. % 5.56/5.74 apply (zenon_L66_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H56 | zenon_intro zenon_Hfc ]. % 5.56/5.74 apply (zenon_L67_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H65 | zenon_intro zenon_H5b ]. % 5.56/5.74 apply (zenon_L68_); trivial. % 5.56/5.74 exact (zenon_Hf7 zenon_H5b). % 5.56/5.74 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H33 | zenon_intro zenon_H92 ]. % 5.56/5.74 apply (zenon_L20_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H74 | zenon_intro zenon_H93 ]. % 5.56/5.74 apply (zenon_L21_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H4f | zenon_intro zenon_H78 ]. % 5.56/5.74 exact (zenon_H4b zenon_H4f). % 5.56/5.74 apply (zenon_L69_); trivial. % 5.56/5.74 (* end of lemma zenon_L70_ *) % 5.56/5.74 assert (zenon_L71_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hc0 zenon_Hf6 zenon_H20 zenon_H57 zenon_H60 zenon_H86 zenon_H4a zenon_H4c zenon_H4d zenon_H6d zenon_H8e zenon_Hf7 zenon_Hf0 zenon_Hee zenon_H95 zenon_Hed zenon_Hf8 zenon_H8f zenon_H22 zenon_H72 zenon_H63 zenon_H4b zenon_Hf3. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.74 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.56/5.74 apply (zenon_L70_); trivial. % 5.56/5.74 (* end of lemma zenon_L71_ *) % 5.56/5.74 assert (zenon_L72_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H60 zenon_Hca zenon_Hfd. % 5.56/5.74 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e0)) = (op (e3) (e3)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hfd. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H8a. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e0)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_Hfe. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H60. % 5.56/5.74 cut (((e3) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hff]. % 5.56/5.74 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 apply zenon_Hff. apply sym_equal. exact zenon_Hca. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 apply zenon_H8b. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L72_ *) % 5.56/5.74 assert (zenon_L73_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H100 zenon_H60 zenon_Hfd zenon_Hed zenon_H22 zenon_Hee zenon_H95 zenon_H63 zenon_H64 zenon_Hf8. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H3d | zenon_intro zenon_Hfb ]. % 5.56/5.74 apply (zenon_L66_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H56 | zenon_intro zenon_Hfc ]. % 5.56/5.74 apply (zenon_L67_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H65 | zenon_intro zenon_H5b ]. % 5.56/5.74 apply (zenon_L15_); trivial. % 5.56/5.74 exact (zenon_Hf7 zenon_H5b). % 5.56/5.74 apply (zenon_L72_); trivial. % 5.56/5.74 (* end of lemma zenon_L73_ *) % 5.56/5.74 assert (zenon_L74_ : ((op (e2) (e2)) = (e2)) -> ((op (e1) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H52 zenon_H73 zenon_H45. % 5.56/5.74 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H101 | zenon_intro zenon_H102 ]. % 5.56/5.74 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e1) (e2)) = (op (e2) (e2)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H45. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H101. % 5.56/5.74 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 5.56/5.74 cut (((op (e2) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e1) (e2)))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H103. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H52. % 5.56/5.74 cut (((e2) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 5.56/5.74 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 5.56/5.74 congruence. % 5.56/5.74 apply zenon_H102. apply refl_equal. % 5.56/5.74 apply zenon_H104. apply sym_equal. exact zenon_H73. % 5.56/5.74 apply zenon_H102. apply refl_equal. % 5.56/5.74 apply zenon_H102. apply refl_equal. % 5.56/5.74 (* end of lemma zenon_L74_ *) % 5.56/5.74 assert (zenon_L75_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H105 zenon_H63 zenon_H31 zenon_H25 zenon_H45 zenon_H52 zenon_H95 zenon_H97. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.56/5.74 apply (zenon_L18_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.56/5.74 exact (zenon_H25 zenon_H2e). % 5.56/5.74 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.56/5.74 apply (zenon_L74_); trivial. % 5.56/5.74 apply (zenon_L30_); trivial. % 5.56/5.74 (* end of lemma zenon_L75_ *) % 5.56/5.74 assert (zenon_L76_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> False). % 5.56/5.74 do 0 intro. intros zenon_H2f zenon_H105 zenon_H63 zenon_H25 zenon_H45 zenon_H52 zenon_H95 zenon_H97. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.56/5.74 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H31. zenon_intro zenon_H24. % 5.56/5.74 apply (zenon_L75_); trivial. % 5.56/5.74 (* end of lemma zenon_L76_ *) % 5.56/5.74 assert (zenon_L77_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hde zenon_H97 zenon_H45 zenon_H25 zenon_H63 zenon_H105 zenon_H72 zenon_H95 zenon_H9a zenon_H86 zenon_H22 zenon_H6d zenon_Hb8 zenon_Hb7 zenon_H52 zenon_Hd9 zenon_Hb4 zenon_H57 zenon_Hce zenon_H60. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.74 apply (zenon_L16_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.74 apply (zenon_L76_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.74 apply (zenon_L31_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.74 apply (zenon_L32_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.74 apply (zenon_L34_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.74 apply (zenon_L9_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.74 apply (zenon_L59_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.74 apply (zenon_L44_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.74 apply (zenon_L48_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.74 apply (zenon_L61_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.74 apply (zenon_L62_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.74 apply (zenon_L52_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.74 apply (zenon_L53_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.74 apply (zenon_L54_); trivial. % 5.56/5.74 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.74 apply (zenon_L56_); trivial. % 5.56/5.74 apply (zenon_L57_); trivial. % 5.56/5.74 (* end of lemma zenon_L77_ *) % 5.56/5.74 assert (zenon_L78_ : ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e3)) -> (~((e2) = (e3))) -> False). % 5.56/5.74 do 0 intro. intros zenon_Hbe zenon_H108 zenon_H86. % 5.56/5.74 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.74 cut (((e3) = (e3)) = ((e2) = (e3))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H86. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_H6e. % 5.56/5.74 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.74 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 5.56/5.74 congruence. % 5.56/5.74 cut (((op (e2) (e0)) = (e2)) = ((e3) = (e2))). % 5.56/5.74 intro zenon_D_pnotp. % 5.56/5.74 apply zenon_H87. % 5.56/5.74 rewrite <- zenon_D_pnotp. % 5.56/5.74 exact zenon_Hbe. % 5.56/5.74 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.75 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 5.56/5.75 congruence. % 5.56/5.75 exact (zenon_H109 zenon_H108). % 5.56/5.75 apply zenon_H62. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 (* end of lemma zenon_L78_ *) % 5.56/5.75 assert (zenon_L79_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H2f zenon_H10a zenon_Hb8 zenon_H6d zenon_H86 zenon_Hbe zenon_H60 zenon_Hfd. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H31. zenon_intro zenon_H24. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.56/5.75 exact (zenon_Hb8 zenon_Hba). % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.56/5.75 apply (zenon_L19_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.56/5.75 apply (zenon_L78_); trivial. % 5.56/5.75 apply (zenon_L72_); trivial. % 5.56/5.75 (* end of lemma zenon_L79_ *) % 5.56/5.75 assert (zenon_L80_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H10d zenon_H86 zenon_Hbe zenon_H9d zenon_Ha3 zenon_H4d zenon_H60 zenon_Hce. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H108 | zenon_intro zenon_H10e ]. % 5.56/5.75 apply (zenon_L78_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H10f ]. % 5.56/5.75 apply (zenon_L41_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H51 | zenon_intro zenon_Hcd ]. % 5.56/5.75 exact (zenon_H4d zenon_H51). % 5.56/5.75 apply (zenon_L55_); trivial. % 5.56/5.75 (* end of lemma zenon_L80_ *) % 5.56/5.75 assert (zenon_L81_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hd7 zenon_H10d zenon_H86 zenon_Hbe zenon_H9d zenon_H4d zenon_H60 zenon_Hce. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.75 apply (zenon_L80_); trivial. % 5.56/5.75 (* end of lemma zenon_L81_ *) % 5.56/5.75 assert (zenon_L82_ : (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e1)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H110 zenon_Hbe zenon_Hc2. % 5.56/5.75 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e1)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H110. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_Hbe. % 5.56/5.75 cut (((e2) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 5.56/5.75 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_Hf2. apply refl_equal. % 5.56/5.75 apply zenon_H111. apply sym_equal. exact zenon_Hc2. % 5.56/5.75 (* end of lemma zenon_L82_ *) % 5.56/5.75 assert (zenon_L83_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hc0 zenon_H110 zenon_Hbe. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.75 apply (zenon_L82_); trivial. % 5.56/5.75 (* end of lemma zenon_L83_ *) % 5.56/5.75 assert (zenon_L84_ : (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hf0 zenon_Hbe zenon_H64. % 5.56/5.75 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e3)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_Hf0. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_Hbe. % 5.56/5.75 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 5.56/5.75 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_Hf2. apply refl_equal. % 5.56/5.75 apply zenon_H112. apply sym_equal. exact zenon_H64. % 5.56/5.75 (* end of lemma zenon_L84_ *) % 5.56/5.75 assert (zenon_L85_ : (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H113 zenon_Hbe zenon_H52. % 5.56/5.75 cut (((op (e2) (e0)) = (e2)) = ((op (e2) (e0)) = (op (e2) (e2)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H113. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_Hbe. % 5.56/5.75 cut (((e2) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Hda]. % 5.56/5.75 cut (((op (e2) (e0)) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_Hf2. apply refl_equal. % 5.56/5.75 apply zenon_Hda. apply sym_equal. exact zenon_H52. % 5.56/5.75 (* end of lemma zenon_L85_ *) % 5.56/5.75 assert (zenon_L86_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H114 zenon_H21 zenon_H24 zenon_H22 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Hb8 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_H20 zenon_Hfd zenon_H100 zenon_H45. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.75 apply (zenon_L2_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.75 apply (zenon_L16_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H31. zenon_intro zenon_H24. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.56/5.75 apply (zenon_L18_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.56/5.75 exact (zenon_H25 zenon_H2e). % 5.56/5.75 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.56/5.75 apply (zenon_L28_); trivial. % 5.56/5.75 apply (zenon_L30_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.75 apply (zenon_L31_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.75 apply (zenon_L32_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.75 apply (zenon_L34_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.75 apply (zenon_L9_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.75 apply (zenon_L65_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.75 apply (zenon_L44_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.75 apply (zenon_L48_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.75 apply (zenon_L71_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.75 apply (zenon_L51_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.75 apply (zenon_L52_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.75 apply (zenon_L53_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.75 apply (zenon_L54_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.75 apply (zenon_L56_); trivial. % 5.56/5.75 apply (zenon_L57_); trivial. % 5.56/5.75 apply (zenon_L72_); trivial. % 5.56/5.75 apply (zenon_L73_); trivial. % 5.56/5.75 apply (zenon_L77_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.75 apply (zenon_L16_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.75 apply (zenon_L79_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.75 apply (zenon_L31_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.75 apply (zenon_L32_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.75 apply (zenon_L34_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.75 apply (zenon_L9_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.75 apply (zenon_L81_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.75 apply (zenon_L44_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.75 apply (zenon_L48_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.75 apply (zenon_L83_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.75 apply (zenon_L51_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.75 apply (zenon_L52_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.75 apply (zenon_L53_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.75 apply (zenon_L54_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.75 apply (zenon_L56_); trivial. % 5.56/5.75 apply (zenon_L57_); trivial. % 5.56/5.75 apply (zenon_L84_); trivial. % 5.56/5.75 apply (zenon_L65_); trivial. % 5.56/5.75 (* end of lemma zenon_L86_ *) % 5.56/5.75 assert (zenon_L87_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H2f zenon_H2c. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H31. zenon_intro zenon_H24. % 5.56/5.75 exact (zenon_H24 zenon_H2c). % 5.56/5.75 (* end of lemma zenon_L87_ *) % 5.56/5.75 assert (zenon_L88_ : (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e1) (e1)) = (e1)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H118 zenon_H41 zenon_H2c. % 5.56/5.75 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e1) (e1)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H118. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H41. % 5.56/5.75 cut (((e1) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 5.56/5.75 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_H9c. apply refl_equal. % 5.56/5.75 apply zenon_H119. apply sym_equal. exact zenon_H2c. % 5.56/5.75 (* end of lemma zenon_L88_ *) % 5.56/5.75 assert (zenon_L89_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e1) (e1)) = (e1)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H3f zenon_H118 zenon_H2c. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.75 apply (zenon_L88_); trivial. % 5.56/5.75 (* end of lemma zenon_L89_ *) % 5.56/5.75 assert (zenon_L90_ : (((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1))))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H43. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H43). zenon_intro zenon_H2c. zenon_intro zenon_H44. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H2c. zenon_intro zenon_H24. % 5.56/5.75 exact (zenon_H24 zenon_H2c). % 5.56/5.75 (* end of lemma zenon_L90_ *) % 5.56/5.75 assert (zenon_L91_ : (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e1)) = (e1)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H11a zenon_H2c zenon_Ha3. % 5.56/5.75 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e2) (e1)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H11a. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H2c. % 5.56/5.75 cut (((e1) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 5.56/5.75 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_H11c. apply refl_equal. % 5.56/5.75 apply zenon_H11b. apply sym_equal. exact zenon_Ha3. % 5.56/5.75 (* end of lemma zenon_L91_ *) % 5.56/5.75 assert (zenon_L92_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hd7 zenon_H11a zenon_H2c. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.75 apply (zenon_L91_); trivial. % 5.56/5.75 (* end of lemma zenon_L92_ *) % 5.56/5.75 assert (zenon_L93_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hc0 zenon_H2c. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.56/5.75 exact (zenon_H24 zenon_H2c). % 5.56/5.75 (* end of lemma zenon_L93_ *) % 5.56/5.75 assert (zenon_L94_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> ((op (e1) (e1)) = (e1)) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hcb zenon_H2c. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.56/5.75 exact (zenon_H24 zenon_H2c). % 5.56/5.75 (* end of lemma zenon_L94_ *) % 5.56/5.75 assert (zenon_L95_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hde zenon_H72 zenon_H118 zenon_H11a zenon_H86 zenon_H22 zenon_H6d zenon_Hb8 zenon_Hb7 zenon_Hb4 zenon_H2c zenon_Hce zenon_H60. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.75 apply (zenon_L16_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.75 apply (zenon_L87_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.75 apply (zenon_L31_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.75 apply (zenon_L32_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.75 apply (zenon_L89_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.75 apply (zenon_L90_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.75 apply (zenon_L92_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.75 apply (zenon_L44_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.75 apply (zenon_L48_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.75 apply (zenon_L93_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.75 apply (zenon_L51_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.75 apply (zenon_L52_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.75 apply (zenon_L53_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.75 apply (zenon_L94_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.75 apply (zenon_L56_); trivial. % 5.56/5.75 apply (zenon_L57_); trivial. % 5.56/5.75 (* end of lemma zenon_L95_ *) % 5.56/5.75 assert (zenon_L96_ : ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H11d zenon_H114 zenon_H21 zenon_H22 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_H20 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H3d ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.56/5.75 apply (zenon_L86_); trivial. % 5.56/5.75 apply (zenon_L95_); trivial. % 5.56/5.75 apply (zenon_L66_); trivial. % 5.56/5.75 (* end of lemma zenon_L96_ *) % 5.56/5.75 assert (zenon_L97_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H2f zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_H20 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.56/5.75 apply (zenon_L96_); trivial. % 5.56/5.75 (* end of lemma zenon_L97_ *) % 5.56/5.75 assert (zenon_L98_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H4a zenon_H33 zenon_H11f zenon_H77 zenon_H4c zenon_H4d. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 5.56/5.75 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H11f. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H33. % 5.56/5.75 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 5.56/5.75 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_H121. apply refl_equal. % 5.56/5.75 apply zenon_H120. apply sym_equal. exact zenon_H4f. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H47 | zenon_intro zenon_H50 ]. % 5.56/5.75 exact (zenon_H77 zenon_H47). % 5.56/5.75 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 5.56/5.75 exact (zenon_H4c zenon_H52). % 5.56/5.75 exact (zenon_H4d zenon_H51). % 5.56/5.75 (* end of lemma zenon_L98_ *) % 5.56/5.75 assert (zenon_L99_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H41 zenon_H6c zenon_H9d. % 5.56/5.75 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.75 cut (((e3) = (e3)) = ((e1) = (e3))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H9d. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H6e. % 5.56/5.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.75 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 5.56/5.75 congruence. % 5.56/5.75 cut (((op (e1) (e0)) = (e1)) = ((e3) = (e1))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H9e. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H41. % 5.56/5.75 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.75 cut (((op (e1) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 5.56/5.75 congruence. % 5.56/5.75 exact (zenon_H71 zenon_H6c). % 5.56/5.75 apply zenon_H94. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 (* end of lemma zenon_L99_ *) % 5.56/5.75 assert (zenon_L100_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hd6 zenon_H108 zenon_H6d. % 5.56/5.75 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.75 cut (((e3) = (e3)) = ((e0) = (e3))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H6d. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H6e. % 5.56/5.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.75 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 5.56/5.75 congruence. % 5.56/5.75 cut (((op (e2) (e0)) = (e0)) = ((e3) = (e0))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H70. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_Hd6. % 5.56/5.75 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.75 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 5.56/5.75 congruence. % 5.56/5.75 exact (zenon_H109 zenon_H108). % 5.56/5.75 apply zenon_H67. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 (* end of lemma zenon_L100_ *) % 5.56/5.75 assert (zenon_L101_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (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 (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H36 zenon_H10a zenon_Hb8 zenon_H9d zenon_H41 zenon_H6d zenon_H60 zenon_Hfd. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_Hd6. zenon_intro zenon_H4c. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.56/5.75 exact (zenon_Hb8 zenon_Hba). % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.56/5.75 apply (zenon_L99_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.56/5.75 apply (zenon_L100_); trivial. % 5.56/5.75 apply (zenon_L72_); trivial. % 5.56/5.75 (* end of lemma zenon_L101_ *) % 5.56/5.75 assert (zenon_L102_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e3)) -> (~((e1) = (e3))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H42 zenon_Ha1 zenon_H9d. % 5.56/5.75 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.75 cut (((e3) = (e3)) = ((e1) = (e3))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H9d. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H6e. % 5.56/5.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.75 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 5.56/5.75 congruence. % 5.56/5.75 cut (((op (e0) (e1)) = (e1)) = ((e3) = (e1))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H9e. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H42. % 5.56/5.75 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.75 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 5.56/5.75 congruence. % 5.56/5.75 exact (zenon_Ha2 zenon_Ha1). % 5.56/5.75 apply zenon_H94. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 (* end of lemma zenon_L102_ *) % 5.56/5.75 assert (zenon_L103_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H33 zenon_Hb1 zenon_H6d. % 5.56/5.75 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.75 cut (((e3) = (e3)) = ((e0) = (e3))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H6d. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H6e. % 5.56/5.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.75 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 5.56/5.75 congruence. % 5.56/5.75 cut (((op (e0) (e2)) = (e0)) = ((e3) = (e0))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H70. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H33. % 5.56/5.75 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.75 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 5.56/5.75 congruence. % 5.56/5.75 exact (zenon_Hb2 zenon_Hb1). % 5.56/5.75 apply zenon_H67. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 (* end of lemma zenon_L103_ *) % 5.56/5.75 assert (zenon_L104_ : (((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). % 5.56/5.75 do 0 intro. intros zenon_Hb7 zenon_Hb8 zenon_H9d zenon_H42 zenon_H6d zenon_H33 zenon_H60 zenon_Hb4. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.56/5.75 exact (zenon_Hb8 zenon_Hba). % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.56/5.75 apply (zenon_L102_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.56/5.75 apply (zenon_L103_); trivial. % 5.56/5.75 apply (zenon_L46_); trivial. % 5.56/5.75 (* end of lemma zenon_L104_ *) % 5.56/5.75 assert (zenon_L105_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H3f zenon_Hb7 zenon_Hb8 zenon_H9d zenon_H6d zenon_H33 zenon_H60 zenon_Hb4. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.75 apply (zenon_L104_); trivial. % 5.56/5.75 (* end of lemma zenon_L105_ *) % 5.56/5.75 assert (zenon_L106_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hd7 zenon_H9f zenon_H41. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.75 apply (zenon_L38_); trivial. % 5.56/5.75 (* end of lemma zenon_L106_ *) % 5.56/5.75 assert (zenon_L107_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H116 zenon_Hbe zenon_Hf0 zenon_H11f zenon_H33 zenon_H77 zenon_H4c zenon_H4a. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.75 apply (zenon_L98_); trivial. % 5.56/5.75 apply (zenon_L84_); trivial. % 5.56/5.75 (* end of lemma zenon_L107_ *) % 5.56/5.75 assert (zenon_L108_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((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)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H117 zenon_H113 zenon_H4a zenon_H77 zenon_H33 zenon_H11f zenon_Hf0 zenon_Hbe zenon_H116. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.75 apply (zenon_L107_); trivial. % 5.56/5.75 apply (zenon_L85_); trivial. % 5.56/5.75 (* end of lemma zenon_L108_ *) % 5.56/5.75 assert (zenon_L109_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((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)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hbc zenon_H117 zenon_H113 zenon_H4a zenon_H77 zenon_H33 zenon_H11f zenon_Hf0 zenon_H116. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.75 apply (zenon_L108_); trivial. % 5.56/5.75 (* end of lemma zenon_L109_ *) % 5.56/5.75 assert (zenon_L110_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1))))) -> (((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))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hc0 zenon_H8e zenon_H9d zenon_H41 zenon_H26 zenon_H86 zenon_H60 zenon_H57. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.56/5.75 apply (zenon_L99_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.56/5.75 exact (zenon_H26 zenon_H2d). % 5.56/5.75 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.56/5.75 apply (zenon_L26_); trivial. % 5.56/5.75 apply (zenon_L27_); trivial. % 5.56/5.75 (* end of lemma zenon_L110_ *) % 5.56/5.75 assert (zenon_L111_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (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) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e2) (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) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H20 zenon_H63 zenon_H8e zenon_H86 zenon_H72 zenon_H8f zenon_H97 zenon_H105 zenon_H9a zenon_H9f zenon_Ha7 zenon_Haa zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H6d zenon_H9d zenon_Hb8 zenon_Hb7 zenon_H116 zenon_Hf0 zenon_H11f zenon_H33 zenon_H77 zenon_H4a zenon_H113 zenon_H117 zenon_Hd9 zenon_Hb4 zenon_H57 zenon_H60 zenon_H52. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.75 apply (zenon_L16_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.75 apply (zenon_L97_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.75 apply (zenon_L58_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.75 apply (zenon_L32_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.75 apply (zenon_L105_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.75 apply (zenon_L9_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.75 apply (zenon_L59_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.75 apply (zenon_L44_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.75 apply (zenon_L109_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.75 apply (zenon_L61_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.75 apply (zenon_L62_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.75 apply (zenon_L52_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.75 apply (zenon_L53_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.75 apply (zenon_L54_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.75 apply (zenon_L63_); trivial. % 5.56/5.75 apply (zenon_L57_); trivial. % 5.56/5.75 (* end of lemma zenon_L111_ *) % 5.56/5.75 assert (zenon_L112_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> ((op (e3) (e0)) = (e0)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H122 zenon_H31 zenon_H39. % 5.56/5.75 cut (((op (e1) (e0)) = (e0)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H122. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H31. % 5.56/5.75 cut (((e0) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 5.56/5.75 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_H9c. apply refl_equal. % 5.56/5.75 apply zenon_H3a. apply sym_equal. exact zenon_H39. % 5.56/5.75 (* end of lemma zenon_L112_ *) % 5.56/5.75 assert (zenon_L113_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H123 zenon_H22 zenon_H124. % 5.56/5.75 cut (((op (e0) (e1)) = (e0)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H123. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H22. % 5.56/5.75 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H125]. % 5.56/5.75 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_H2a. apply refl_equal. % 5.56/5.75 apply zenon_H125. apply sym_equal. exact zenon_H124. % 5.56/5.75 (* end of lemma zenon_L113_ *) % 5.56/5.75 assert (zenon_L114_ : ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hc2 zenon_Ha4 zenon_H86. % 5.56/5.75 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.75 cut (((e3) = (e3)) = ((e2) = (e3))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H86. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H6e. % 5.56/5.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.75 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 5.56/5.75 congruence. % 5.56/5.75 cut (((op (e2) (e1)) = (e2)) = ((e3) = (e2))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H87. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_Hc2. % 5.56/5.75 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.75 cut (((op (e2) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 5.56/5.75 congruence. % 5.56/5.75 exact (zenon_Ha5 zenon_Ha4). % 5.56/5.75 apply zenon_H62. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 (* end of lemma zenon_L114_ *) % 5.56/5.75 assert (zenon_L115_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e0)) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_Haa zenon_H6d zenon_Hf7 zenon_H4a zenon_H4b zenon_H4c zenon_H4d zenon_H123 zenon_H22 zenon_H122 zenon_H31 zenon_H126 zenon_H86 zenon_Hc2 zenon_H60 zenon_Ha7. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hab ]. % 5.56/5.75 apply (zenon_L40_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H2d | zenon_intro zenon_Hac ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H39 | zenon_intro zenon_H127 ]. % 5.56/5.75 apply (zenon_L112_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H124 | zenon_intro zenon_H128 ]. % 5.56/5.75 apply (zenon_L113_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H78 | zenon_intro zenon_H5b ]. % 5.56/5.75 apply (zenon_L25_); trivial. % 5.56/5.75 exact (zenon_Hf7 zenon_H5b). % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha6 ]. % 5.56/5.75 apply (zenon_L114_); trivial. % 5.56/5.75 apply (zenon_L42_); trivial. % 5.56/5.75 (* end of lemma zenon_L115_ *) % 5.56/5.75 assert (zenon_L116_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H2f zenon_Haa zenon_H6d zenon_Hf7 zenon_H4a zenon_H4b zenon_H4c zenon_H4d zenon_H123 zenon_H122 zenon_H126 zenon_H86 zenon_Hc2 zenon_H60 zenon_Ha7. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H31. zenon_intro zenon_H24. % 5.56/5.75 apply (zenon_L115_); trivial. % 5.56/5.75 (* end of lemma zenon_L116_ *) % 5.56/5.75 assert (zenon_L117_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e1)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hbc zenon_H110 zenon_Hc2. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.75 apply (zenon_L82_); trivial. % 5.56/5.75 (* end of lemma zenon_L117_ *) % 5.56/5.75 assert (zenon_L118_ : (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H129 zenon_Hc2 zenon_H64. % 5.56/5.75 cut (((op (e2) (e1)) = (e2)) = ((op (e2) (e1)) = (op (e2) (e3)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H129. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_Hc2. % 5.56/5.75 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 5.56/5.75 cut (((op (e2) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_Hdb. apply refl_equal. % 5.56/5.75 apply zenon_H112. apply sym_equal. exact zenon_H64. % 5.56/5.75 (* end of lemma zenon_L118_ *) % 5.56/5.75 assert (zenon_L119_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H12a zenon_H110 zenon_H116 zenon_Hbe zenon_Hf0 zenon_H11f zenon_H33 zenon_H4a zenon_H113 zenon_H117. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.75 apply (zenon_L108_); trivial. % 5.56/5.75 apply (zenon_L82_); trivial. % 5.56/5.75 (* end of lemma zenon_L119_ *) % 5.56/5.75 assert (zenon_L120_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H11f zenon_H33 zenon_H41 zenon_Hb8 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H20. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.75 apply (zenon_L16_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.75 apply (zenon_L97_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.75 apply (zenon_L101_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.75 apply (zenon_L32_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.75 apply (zenon_L105_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.75 apply (zenon_L9_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.75 apply (zenon_L106_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.75 apply (zenon_L44_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.75 apply (zenon_L109_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.75 apply (zenon_L110_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.75 apply (zenon_L51_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.75 apply (zenon_L52_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.75 apply (zenon_L53_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.75 apply (zenon_L54_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.75 apply (zenon_L56_); trivial. % 5.56/5.75 apply (zenon_L57_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.75 apply (zenon_L16_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.75 apply (zenon_L116_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.75 apply (zenon_L101_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.75 apply (zenon_L32_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.75 apply (zenon_L105_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.75 apply (zenon_L9_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.75 apply (zenon_L106_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.75 apply (zenon_L44_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.75 apply (zenon_L117_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.75 apply (zenon_L110_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.75 apply (zenon_L51_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.75 apply (zenon_L52_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.75 apply (zenon_L53_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.75 apply (zenon_L54_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.75 apply (zenon_L56_); trivial. % 5.56/5.75 apply (zenon_L57_); trivial. % 5.56/5.75 apply (zenon_L72_); trivial. % 5.56/5.75 apply (zenon_L118_); trivial. % 5.56/5.75 apply (zenon_L60_); trivial. % 5.56/5.75 apply (zenon_L119_); trivial. % 5.56/5.75 apply (zenon_L33_); trivial. % 5.56/5.75 (* end of lemma zenon_L120_ *) % 5.56/5.75 assert (zenon_L121_ : ((op (e2) (e0)) = (e0)) -> ((op (e2) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hd6 zenon_H12b zenon_Hee. % 5.56/5.75 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H12c | zenon_intro zenon_H94 ]. % 5.56/5.75 cut (((e1) = (e1)) = ((e0) = (e1))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_Hee. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H12c. % 5.56/5.75 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.75 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 5.56/5.75 congruence. % 5.56/5.75 cut (((op (e2) (e0)) = (e0)) = ((e1) = (e0))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H12d. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_Hd6. % 5.56/5.75 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.75 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 5.56/5.75 congruence. % 5.56/5.75 exact (zenon_H12e zenon_H12b). % 5.56/5.75 apply zenon_H67. apply refl_equal. % 5.56/5.75 apply zenon_H94. apply refl_equal. % 5.56/5.75 apply zenon_H94. apply refl_equal. % 5.56/5.75 (* end of lemma zenon_L121_ *) % 5.56/5.75 assert (zenon_L122_ : (~((e0) = (e1))) -> ((op (e2) (e1)) = (e1)) -> ((op (e2) (e1)) = (e0)) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hee zenon_Ha3 zenon_H12f. % 5.56/5.75 cut (((op (e2) (e1)) = (e1)) = ((e0) = (e1))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_Hee. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_Ha3. % 5.56/5.75 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.75 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H130]. % 5.56/5.75 congruence. % 5.56/5.75 exact (zenon_H130 zenon_H12f). % 5.56/5.75 apply zenon_H94. apply refl_equal. % 5.56/5.75 (* end of lemma zenon_L122_ *) % 5.56/5.75 assert (zenon_L123_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H131 zenon_H2e. % 5.56/5.75 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 5.56/5.75 cut (((op (e1) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 5.56/5.75 congruence. % 5.56/5.75 exact (zenon_H25 zenon_H2e). % 5.56/5.75 exact (zenon_H25 zenon_H2e). % 5.56/5.75 (* end of lemma zenon_L123_ *) % 5.56/5.75 assert (zenon_L124_ : ((op (e3) (e1)) = (e0)) -> ((op (e2) (e2)) = (e3)) -> ((op (e1) (e1)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H124 zenon_H51 zenon_H2e. % 5.56/5.75 apply (zenon_notand_s _ _ ax22); [ zenon_intro zenon_H133 | zenon_intro zenon_H132 ]. % 5.56/5.75 apply zenon_H133. apply sym_equal. exact zenon_H2e. % 5.56/5.75 apply (zenon_notand_s _ _ zenon_H132); [ zenon_intro zenon_H135 | zenon_intro zenon_H134 ]. % 5.56/5.75 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H136 | zenon_intro zenon_H137 ]. % 5.56/5.75 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e3) = (op (op (e1) (e1)) (op (e1) (e1))))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H135. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H136. % 5.56/5.75 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 5.56/5.75 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H138]. % 5.56/5.75 congruence. % 5.56/5.75 cut (((op (e2) (e2)) = (e3)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e3))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H138. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H51. % 5.56/5.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.75 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 5.56/5.75 congruence. % 5.56/5.75 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H136 | zenon_intro zenon_H137 ]. % 5.56/5.75 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H139. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H136. % 5.56/5.75 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 5.56/5.75 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 5.56/5.75 congruence. % 5.56/5.75 apply (zenon_L123_); trivial. % 5.56/5.75 apply zenon_H137. apply refl_equal. % 5.56/5.75 apply zenon_H137. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 apply zenon_H137. apply refl_equal. % 5.56/5.75 apply zenon_H137. apply refl_equal. % 5.56/5.75 elim (classic ((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_H13a | zenon_intro zenon_H13b ]. % 5.56/5.75 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1))) = ((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H134. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H13a. % 5.56/5.75 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 5.56/5.75 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 5.56/5.75 congruence. % 5.56/5.75 cut (((op (e3) (e1)) = (e0)) = ((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (e0))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H13c. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H124. % 5.56/5.75 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.75 cut (((op (e3) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 5.56/5.75 congruence. % 5.56/5.75 elim (classic ((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_H13a | zenon_intro zenon_H13b ]. % 5.56/5.75 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1))) = ((op (e3) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H13d. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H13a. % 5.56/5.75 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 5.56/5.75 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13e]. % 5.56/5.75 congruence. % 5.56/5.75 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.75 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H138]. % 5.56/5.75 congruence. % 5.56/5.75 cut (((op (e2) (e2)) = (e3)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e3))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H138. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H51. % 5.56/5.75 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.75 cut (((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 5.56/5.75 congruence. % 5.56/5.75 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H136 | zenon_intro zenon_H137 ]. % 5.56/5.75 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e2) (e2)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H139. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H136. % 5.56/5.75 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 5.56/5.75 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 5.56/5.75 congruence. % 5.56/5.75 apply (zenon_L123_); trivial. % 5.56/5.75 apply zenon_H137. apply refl_equal. % 5.56/5.75 apply zenon_H137. apply refl_equal. % 5.56/5.75 apply zenon_H6f. apply refl_equal. % 5.56/5.75 apply zenon_H94. apply refl_equal. % 5.56/5.75 apply zenon_H13b. apply refl_equal. % 5.56/5.75 apply zenon_H13b. apply refl_equal. % 5.56/5.75 apply zenon_H67. apply refl_equal. % 5.56/5.75 apply zenon_H13b. apply refl_equal. % 5.56/5.75 apply zenon_H13b. apply refl_equal. % 5.56/5.75 (* end of lemma zenon_L124_ *) % 5.56/5.75 assert (zenon_L125_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H10d zenon_H6d zenon_Hd6 zenon_H9d zenon_Ha3 zenon_H26 zenon_H124 zenon_H24 zenon_H13f zenon_H21 zenon_H60 zenon_Hce. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H108 | zenon_intro zenon_H10e ]. % 5.56/5.75 apply (zenon_L100_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H10f ]. % 5.56/5.75 apply (zenon_L41_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H51 | zenon_intro zenon_Hcd ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 5.56/5.75 exact (zenon_H13f zenon_H28). % 5.56/5.75 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 5.56/5.75 exact (zenon_H24 zenon_H2c). % 5.56/5.75 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 5.56/5.75 apply (zenon_L124_); trivial. % 5.56/5.75 exact (zenon_H26 zenon_H2d). % 5.56/5.75 apply (zenon_L55_); trivial. % 5.56/5.75 (* end of lemma zenon_L125_ *) % 5.56/5.75 assert (zenon_L126_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e3)) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e2) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H140 zenon_Ha1 zenon_Hee zenon_H10d zenon_H6d zenon_Hd6 zenon_H9d zenon_Ha3 zenon_H26 zenon_H24 zenon_H13f zenon_H21 zenon_H60 zenon_Hce. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.56/5.75 apply (zenon_L40_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.56/5.75 exact (zenon_H13f zenon_H28). % 5.56/5.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.56/5.75 apply (zenon_L122_); trivial. % 5.56/5.75 apply (zenon_L125_); trivial. % 5.56/5.75 (* end of lemma zenon_L126_ *) % 5.56/5.75 assert (zenon_L127_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e0)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H143 zenon_H39 zenon_H124. % 5.56/5.75 cut (((op (e3) (e0)) = (e0)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H143. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H39. % 5.56/5.75 cut (((e0) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H125]. % 5.56/5.75 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_Hf5. apply refl_equal. % 5.56/5.75 apply zenon_H125. apply sym_equal. exact zenon_H124. % 5.56/5.75 (* end of lemma zenon_L127_ *) % 5.56/5.75 assert (zenon_L128_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hf6 zenon_H33 zenon_H10d zenon_H26 zenon_H21 zenon_H140 zenon_H20 zenon_H6d zenon_H9d zenon_H46 zenon_H57 zenon_H60 zenon_H8e zenon_H72 zenon_H9f zenon_H24 zenon_Ha7 zenon_Haa zenon_Hb8 zenon_H86 zenon_Hb4 zenon_Hb7 zenon_H97 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_H13f zenon_Ha3 zenon_Hee zenon_H143. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.56/5.75 exact (zenon_H20 zenon_H1f). % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.56/5.75 apply (zenon_L36_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.56/5.75 exact (zenon_Hb8 zenon_Hba). % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.56/5.75 apply (zenon_L126_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.56/5.75 apply (zenon_L103_); trivial. % 5.56/5.75 apply (zenon_L46_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.56/5.75 apply (zenon_L65_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.56/5.75 exact (zenon_H13f zenon_H28). % 5.56/5.75 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.56/5.75 apply (zenon_L122_); trivial. % 5.56/5.75 apply (zenon_L127_); trivial. % 5.56/5.75 (* end of lemma zenon_L128_ *) % 5.56/5.75 assert (zenon_L129_ : (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H97 zenon_H64 zenon_H144. % 5.56/5.75 cut (((op (e2) (e3)) = (e2)) = ((e1) = (e2))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H97. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H64. % 5.56/5.75 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.75 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 5.56/5.75 congruence. % 5.56/5.75 exact (zenon_H145 zenon_H144). % 5.56/5.75 apply zenon_H62. apply refl_equal. % 5.56/5.75 (* end of lemma zenon_L129_ *) % 5.56/5.75 assert (zenon_L130_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H146 zenon_Hd6 zenon_H143 zenon_Hee zenon_H13f zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_H86 zenon_Hb8 zenon_Haa zenon_Ha7 zenon_H24 zenon_H9f zenon_H72 zenon_H8e zenon_H60 zenon_H57 zenon_H46 zenon_H9d zenon_H6d zenon_H20 zenon_H140 zenon_H21 zenon_H26 zenon_H10d zenon_H33 zenon_Hf6 zenon_H77 zenon_H97 zenon_H64. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H12b | zenon_intro zenon_H147 ]. % 5.56/5.75 apply (zenon_L121_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H148 ]. % 5.56/5.75 apply (zenon_L128_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H47 | zenon_intro zenon_H144 ]. % 5.56/5.75 exact (zenon_H77 zenon_H47). % 5.56/5.75 apply (zenon_L129_); trivial. % 5.56/5.75 (* end of lemma zenon_L130_ *) % 5.56/5.75 assert (zenon_L131_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H36 zenon_H146 zenon_H143 zenon_Hee zenon_H13f zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_H86 zenon_Hb8 zenon_Haa zenon_Ha7 zenon_H24 zenon_H9f zenon_H72 zenon_H8e zenon_H60 zenon_H57 zenon_H46 zenon_H9d zenon_H6d zenon_H20 zenon_H140 zenon_H21 zenon_H26 zenon_H10d zenon_Hf6 zenon_H77 zenon_H97 zenon_H64. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.56/5.75 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_Hd6. zenon_intro zenon_H4c. % 5.56/5.75 apply (zenon_L130_); trivial. % 5.56/5.75 (* end of lemma zenon_L131_ *) % 5.56/5.75 assert (zenon_L132_ : (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e1)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H11f zenon_H149 zenon_H47. % 5.56/5.75 cut (((op (e0) (e2)) = (e1)) = ((op (e0) (e2)) = (op (e2) (e2)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H11f. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H149. % 5.56/5.75 cut (((e1) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 5.56/5.75 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_H121. apply refl_equal. % 5.56/5.75 apply zenon_H48. apply sym_equal. exact zenon_H47. % 5.56/5.75 (* end of lemma zenon_L132_ *) % 5.56/5.75 assert (zenon_L133_ : (((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) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H4a zenon_H4b zenon_H149 zenon_H11f zenon_H4c zenon_H4d. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 5.56/5.75 exact (zenon_H4b zenon_H4f). % 5.56/5.75 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H47 | zenon_intro zenon_H50 ]. % 5.56/5.75 apply (zenon_L132_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 5.56/5.75 exact (zenon_H4c zenon_H52). % 5.56/5.75 exact (zenon_H4d zenon_H51). % 5.56/5.75 (* end of lemma zenon_L133_ *) % 5.56/5.75 assert (zenon_L134_ : ((op (e1) (e3)) = (e1)) -> ((op (e0) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H95 zenon_H14a zenon_H14b. % 5.56/5.75 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H14c | zenon_intro zenon_H5d ]. % 5.56/5.75 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H14b. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H14c. % 5.56/5.75 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 5.56/5.75 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 5.56/5.75 congruence. % 5.56/5.75 cut (((op (e1) (e3)) = (e1)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H14d. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H95. % 5.56/5.75 cut (((e1) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14e]. % 5.56/5.75 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_H5d. apply refl_equal. % 5.56/5.75 apply zenon_H14e. apply sym_equal. exact zenon_H14a. % 5.56/5.75 apply zenon_H5d. apply refl_equal. % 5.56/5.75 apply zenon_H5d. apply refl_equal. % 5.56/5.75 (* end of lemma zenon_L134_ *) % 5.56/5.75 assert (zenon_L135_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H14f zenon_H150 zenon_Hb4 zenon_H60 zenon_H33 zenon_H6d zenon_H9d zenon_Hb8 zenon_Hb7 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H95 zenon_H14b. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.56/5.75 exact (zenon_H150 zenon_H152). % 5.56/5.75 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.56/5.75 apply (zenon_L104_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.56/5.75 apply (zenon_L133_); trivial. % 5.56/5.75 apply (zenon_L134_); trivial. % 5.56/5.75 (* end of lemma zenon_L135_ *) % 5.56/5.75 assert (zenon_L136_ : (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e0) (e3)) = (e0)) -> False). % 5.56/5.75 do 0 intro. intros zenon_H154 zenon_H33 zenon_H3d. % 5.56/5.75 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e0) (e3)))). % 5.56/5.75 intro zenon_D_pnotp. % 5.56/5.75 apply zenon_H154. % 5.56/5.75 rewrite <- zenon_D_pnotp. % 5.56/5.75 exact zenon_H33. % 5.56/5.75 cut (((e0) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 5.56/5.75 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 5.56/5.75 congruence. % 5.56/5.75 apply zenon_H121. apply refl_equal. % 5.56/5.75 apply zenon_H54. apply sym_equal. exact zenon_H3d. % 5.56/5.75 (* end of lemma zenon_L136_ *) % 5.56/5.75 assert (zenon_L137_ : (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 5.56/5.75 do 0 intro. intros zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H8e zenon_H57 zenon_H86 zenon_H72 zenon_H8f zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9f zenon_Ha7 zenon_Haa zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf0 zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H77 zenon_H14f zenon_H95 zenon_H14b zenon_H4b zenon_H11f zenon_H4a zenon_Hb8 zenon_H9d zenon_H6d zenon_H33 zenon_Hb4 zenon_H60 zenon_Hb7 zenon_H150 zenon_H100 zenon_Hfd zenon_H154 zenon_Hee zenon_H63 zenon_Hf8 zenon_H116. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.75 apply (zenon_L135_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H3d | zenon_intro zenon_Hfb ]. % 5.56/5.75 apply (zenon_L136_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H56 | zenon_intro zenon_Hfc ]. % 5.56/5.75 apply (zenon_L67_); trivial. % 5.56/5.75 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H65 | zenon_intro zenon_H5b ]. % 5.56/5.75 apply (zenon_L15_); trivial. % 5.56/5.75 exact (zenon_Hf7 zenon_H5b). % 5.56/5.75 apply (zenon_L72_); trivial. % 5.56/5.75 apply (zenon_L111_); trivial. % 5.56/5.75 (* end of lemma zenon_L137_ *) % 5.56/5.75 assert (zenon_L138_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.56/5.75 do 0 intro. intros zenon_Hc0 zenon_H129 zenon_H64. % 5.56/5.75 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.75 apply (zenon_L118_); trivial. % 5.56/5.75 (* end of lemma zenon_L138_ *) % 5.56/5.75 assert (zenon_L139_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (((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) (e3)) = (op (e1) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H4a zenon_H77 zenon_H33 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H24 zenon_Hb8 zenon_H143 zenon_H140 zenon_H13f zenon_H26 zenon_H146 zenon_H14f zenon_H14b zenon_H4b zenon_H150 zenon_H154 zenon_H155 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H20. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.76 apply (zenon_L98_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.76 apply (zenon_L16_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.76 apply (zenon_L97_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H41 | zenon_intro zenon_H156 ]. % 5.56/5.76 apply (zenon_L120_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H2c | zenon_intro zenon_H157 ]. % 5.56/5.76 exact (zenon_H24 zenon_H2c). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H46 | zenon_intro zenon_H95 ]. % 5.56/5.76 apply (zenon_L131_); trivial. % 5.56/5.76 apply (zenon_L137_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.76 apply (zenon_L32_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.76 apply (zenon_L105_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.76 apply (zenon_L9_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.76 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.76 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.76 apply (zenon_L128_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.76 apply (zenon_L44_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.76 apply (zenon_L109_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.76 apply (zenon_L138_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.76 apply (zenon_L51_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.76 apply (zenon_L52_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.76 apply (zenon_L53_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.76 apply (zenon_L54_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.76 apply (zenon_L56_); trivial. % 5.56/5.76 apply (zenon_L57_); trivial. % 5.56/5.76 apply (zenon_L111_); trivial. % 5.56/5.76 (* end of lemma zenon_L139_ *) % 5.56/5.76 assert (zenon_L140_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H10d zenon_H6d zenon_Hd6 zenon_H86 zenon_Hc2 zenon_H4d zenon_H60 zenon_Hce. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H108 | zenon_intro zenon_H10e ]. % 5.56/5.76 apply (zenon_L100_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H10f ]. % 5.56/5.76 apply (zenon_L114_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H51 | zenon_intro zenon_Hcd ]. % 5.56/5.76 exact (zenon_H4d zenon_H51). % 5.56/5.76 apply (zenon_L55_); trivial. % 5.56/5.76 (* end of lemma zenon_L140_ *) % 5.56/5.76 assert (zenon_L141_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H36 zenon_H10d zenon_H6d zenon_H86 zenon_Hc2 zenon_H4d zenon_H60 zenon_Hce. % 5.56/5.76 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.56/5.76 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_Hd6. zenon_intro zenon_H4c. % 5.56/5.76 apply (zenon_L140_); trivial. % 5.56/5.76 (* end of lemma zenon_L141_ *) % 5.56/5.76 assert (zenon_L142_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H116 zenon_Hc2 zenon_H129 zenon_H4b zenon_H45 zenon_H46 zenon_H4c zenon_H4a. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.76 apply (zenon_L11_); trivial. % 5.56/5.76 apply (zenon_L118_); trivial. % 5.56/5.76 (* end of lemma zenon_L142_ *) % 5.56/5.76 assert (zenon_L143_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 5.56/5.76 do 0 intro. intros zenon_Hd7 zenon_H116 zenon_Hc2 zenon_H129 zenon_H4b zenon_H45 zenon_H4a. % 5.56/5.76 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.76 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.76 apply (zenon_L142_); trivial. % 5.56/5.76 (* end of lemma zenon_L143_ *) % 5.56/5.76 assert (zenon_L144_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H14f zenon_H150 zenon_H4d zenon_H4c zenon_H4b zenon_H155 zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_Hb8 zenon_H33 zenon_H11f zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H24 zenon_H97 zenon_H73 zenon_H14b. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.56/5.76 exact (zenon_H150 zenon_H152). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.56/5.76 apply (zenon_L104_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.56/5.76 apply (zenon_L133_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H41 | zenon_intro zenon_H156 ]. % 5.56/5.76 apply (zenon_L120_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H2c | zenon_intro zenon_H157 ]. % 5.56/5.76 exact (zenon_H24 zenon_H2c). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H46 | zenon_intro zenon_H95 ]. % 5.56/5.76 apply (zenon_L49_); trivial. % 5.56/5.76 apply (zenon_L134_); trivial. % 5.56/5.76 (* end of lemma zenon_L144_ *) % 5.56/5.76 assert (zenon_L145_ : (~((op (e3) (e3)) = (e0))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.76 do 0 intro. intros zenon_Hf7 zenon_Hc2 zenon_H14b zenon_H97 zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H11f zenon_H33 zenon_Hb8 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hb7 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H20 zenon_H155 zenon_H4b zenon_H4c zenon_H4d zenon_H150 zenon_H14f zenon_Hb4 zenon_H57 zenon_Hce zenon_H60. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.76 apply (zenon_L16_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.76 apply (zenon_L116_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.76 apply (zenon_L141_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.76 apply (zenon_L32_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.76 apply (zenon_L105_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.76 apply (zenon_L9_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.76 apply (zenon_L143_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.76 apply (zenon_L44_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.76 apply (zenon_L117_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.76 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.76 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.56/5.76 apply (zenon_L144_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.76 apply (zenon_L51_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.76 apply (zenon_L52_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.76 apply (zenon_L53_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.76 apply (zenon_L54_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.76 apply (zenon_L56_); trivial. % 5.56/5.76 apply (zenon_L57_); trivial. % 5.56/5.76 (* end of lemma zenon_L145_ *) % 5.56/5.76 assert (zenon_L146_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.56/5.76 do 0 intro. intros zenon_H146 zenon_Hee zenon_Hd6 zenon_H2c zenon_H11a zenon_H77 zenon_H97 zenon_H64. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H12b | zenon_intro zenon_H147 ]. % 5.56/5.76 apply (zenon_L121_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H148 ]. % 5.56/5.76 apply (zenon_L91_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H47 | zenon_intro zenon_H144 ]. % 5.56/5.76 exact (zenon_H77 zenon_H47). % 5.56/5.76 apply (zenon_L129_); trivial. % 5.56/5.76 (* end of lemma zenon_L146_ *) % 5.56/5.76 assert (zenon_L147_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.56/5.76 do 0 intro. intros zenon_H36 zenon_H146 zenon_Hee zenon_H2c zenon_H11a zenon_H77 zenon_H97 zenon_H64. % 5.56/5.76 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.56/5.76 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_Hd6. zenon_intro zenon_H4c. % 5.56/5.76 apply (zenon_L146_); trivial. % 5.56/5.76 (* end of lemma zenon_L147_ *) % 5.56/5.76 assert (zenon_L148_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.76 do 0 intro. intros zenon_Hde zenon_Ha7 zenon_H126 zenon_H122 zenon_H123 zenon_H4c zenon_Hf7 zenon_Haa zenon_H4d zenon_H86 zenon_H6d zenon_H10d zenon_H118 zenon_H4a zenon_H45 zenon_H4b zenon_H129 zenon_H116 zenon_Hc2 zenon_H110 zenon_Hb4 zenon_H2c zenon_Hce zenon_H60. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.76 apply (zenon_L16_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.76 apply (zenon_L116_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.76 apply (zenon_L141_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.76 apply (zenon_L32_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.76 apply (zenon_L89_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.76 apply (zenon_L90_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.76 apply (zenon_L143_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.76 apply (zenon_L44_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.76 apply (zenon_L117_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.76 apply (zenon_L93_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.76 apply (zenon_L51_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.76 apply (zenon_L52_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.76 apply (zenon_L53_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.76 apply (zenon_L94_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.76 apply (zenon_L56_); trivial. % 5.56/5.76 apply (zenon_L57_); trivial. % 5.56/5.76 (* end of lemma zenon_L148_ *) % 5.56/5.76 assert (zenon_L149_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H100 zenon_Hfd zenon_H6d zenon_H126 zenon_H4b zenon_H4c zenon_H4d zenon_H4a zenon_H123 zenon_H122 zenon_H86 zenon_Hc2 zenon_Ha7 zenon_H60 zenon_Haa zenon_Hce zenon_H10d zenon_H2c zenon_H118 zenon_H45 zenon_H129 zenon_H116 zenon_H110 zenon_Hb4 zenon_Hde. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.76 apply (zenon_L148_); trivial. % 5.56/5.76 apply (zenon_L72_); trivial. % 5.56/5.76 (* end of lemma zenon_L149_ *) % 5.56/5.76 assert (zenon_L150_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H117 zenon_Hd9 zenon_H100 zenon_Hfd zenon_H6d zenon_H126 zenon_H4b zenon_H4a zenon_H123 zenon_H122 zenon_H86 zenon_Hc2 zenon_Ha7 zenon_H60 zenon_Haa zenon_Hce zenon_H10d zenon_H2c zenon_H118 zenon_H45 zenon_H129 zenon_H116 zenon_H110 zenon_Hb4 zenon_Hde. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.76 apply (zenon_L149_); trivial. % 5.56/5.76 apply (zenon_L118_); trivial. % 5.56/5.76 apply (zenon_L60_); trivial. % 5.56/5.76 (* end of lemma zenon_L150_ *) % 5.56/5.76 assert (zenon_L151_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H4b zenon_H126 zenon_H20 zenon_H2c zenon_Hee zenon_H11a zenon_H97 zenon_H146 zenon_H60 zenon_H118 zenon_H116 zenon_Hf0 zenon_H113 zenon_H117 zenon_Hb4 zenon_Hce zenon_Hde zenon_H11f zenon_H33 zenon_H4a zenon_Hb8 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hb7 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H9a zenon_H105 zenon_H6d zenon_H8f zenon_H72 zenon_H86 zenon_H57 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H11e. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.76 apply (zenon_L98_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.76 apply (zenon_L16_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.76 apply (zenon_L87_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.76 apply (zenon_L147_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.76 apply (zenon_L32_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.76 apply (zenon_L89_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.76 apply (zenon_L90_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.76 apply (zenon_L92_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.76 apply (zenon_L44_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.76 apply (zenon_L109_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.76 apply (zenon_L93_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.76 apply (zenon_L51_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.76 apply (zenon_L52_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.76 apply (zenon_L53_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.76 apply (zenon_L94_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.76 apply (zenon_L56_); trivial. % 5.56/5.76 apply (zenon_L57_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.76 apply (zenon_L16_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.76 apply (zenon_L97_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.76 apply (zenon_L58_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.76 apply (zenon_L32_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.76 apply (zenon_L105_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.76 apply (zenon_L90_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.76 apply (zenon_L59_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.76 apply (zenon_L44_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.76 apply (zenon_L109_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.76 apply (zenon_L61_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.76 apply (zenon_L62_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.76 apply (zenon_L52_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.76 apply (zenon_L53_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.76 apply (zenon_L54_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.76 apply (zenon_L63_); trivial. % 5.56/5.76 apply (zenon_L57_); trivial. % 5.56/5.76 apply (zenon_L150_); trivial. % 5.56/5.76 (* end of lemma zenon_L151_ *) % 5.56/5.76 assert (zenon_L152_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H4a zenon_H33 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H20 zenon_H158. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H3d ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.76 apply (zenon_L139_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.76 apply (zenon_L145_); trivial. % 5.56/5.76 apply (zenon_L72_); trivial. % 5.56/5.76 apply (zenon_L118_); trivial. % 5.56/5.76 apply (zenon_L60_); trivial. % 5.56/5.76 apply (zenon_L119_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.76 apply (zenon_L137_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.76 apply (zenon_L135_); trivial. % 5.56/5.76 apply (zenon_L118_); trivial. % 5.56/5.76 apply (zenon_L60_); trivial. % 5.56/5.76 apply (zenon_L119_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.76 apply (zenon_L151_); trivial. % 5.56/5.76 apply (zenon_L119_); trivial. % 5.56/5.76 apply (zenon_L120_); trivial. % 5.56/5.76 apply (zenon_L136_); trivial. % 5.56/5.76 (* end of lemma zenon_L152_ *) % 5.56/5.76 assert (zenon_L153_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H36 zenon_H4a zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H20 zenon_H158. % 5.56/5.76 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.56/5.76 apply (zenon_L152_); trivial. % 5.56/5.76 (* end of lemma zenon_L153_ *) % 5.56/5.76 assert (zenon_L154_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H22 zenon_H42 zenon_Hee. % 5.56/5.76 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H12c | zenon_intro zenon_H94 ]. % 5.56/5.76 cut (((e1) = (e1)) = ((e0) = (e1))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_Hee. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H12c. % 5.56/5.76 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.76 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 5.56/5.76 congruence. % 5.56/5.76 cut (((op (e0) (e1)) = (e0)) = ((e1) = (e0))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H12d. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H22. % 5.56/5.76 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.76 cut (((op (e0) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 5.56/5.76 congruence. % 5.56/5.76 exact (zenon_H159 zenon_H42). % 5.56/5.76 apply zenon_H67. apply refl_equal. % 5.56/5.76 apply zenon_H94. apply refl_equal. % 5.56/5.76 apply zenon_H94. apply refl_equal. % 5.56/5.76 (* end of lemma zenon_L154_ *) % 5.56/5.76 assert (zenon_L155_ : ((op (e0) (e1)) = (e1)) -> ((op (e0) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H42 zenon_H15a zenon_H97. % 5.56/5.76 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.56/5.76 cut (((e2) = (e2)) = ((e1) = (e2))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H97. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H69. % 5.56/5.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.76 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 5.56/5.76 congruence. % 5.56/5.76 cut (((op (e0) (e1)) = (e1)) = ((e2) = (e1))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H98. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H42. % 5.56/5.76 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.76 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 5.56/5.76 congruence. % 5.56/5.76 exact (zenon_H15b zenon_H15a). % 5.56/5.76 apply zenon_H94. apply refl_equal. % 5.56/5.76 apply zenon_H62. apply refl_equal. % 5.56/5.76 apply zenon_H62. apply refl_equal. % 5.56/5.76 (* end of lemma zenon_L155_ *) % 5.56/5.76 assert (zenon_L156_ : (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> ((op (e0) (e2)) = (e1)) -> False). % 5.56/5.76 do 0 intro. intros zenon_H97 zenon_Hb0 zenon_H149. % 5.56/5.76 cut (((op (e0) (e2)) = (e2)) = ((e1) = (e2))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H97. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_Hb0. % 5.56/5.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.76 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 5.56/5.76 congruence. % 5.56/5.76 exact (zenon_H15c zenon_H149). % 5.56/5.76 apply zenon_H62. apply refl_equal. % 5.56/5.76 (* end of lemma zenon_L156_ *) % 5.56/5.76 assert (zenon_L157_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))) -> ((op (e2) (e2)) = (e0)) -> False). % 5.56/5.76 do 0 intro. intros zenon_H15d zenon_H4f. % 5.56/5.76 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 5.56/5.76 cut (((op (e2) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H4b]. % 5.56/5.76 congruence. % 5.56/5.76 exact (zenon_H4b zenon_H4f). % 5.56/5.76 exact (zenon_H4b zenon_H4f). % 5.56/5.76 (* end of lemma zenon_L157_ *) % 5.56/5.76 assert (zenon_L158_ : ((op (e3) (e2)) = (e1)) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False). % 5.56/5.76 do 0 intro. intros zenon_H15e zenon_Hba zenon_H4f. % 5.56/5.76 apply (zenon_notand_s _ _ ax10); [ zenon_intro zenon_H120 | zenon_intro zenon_H15f ]. % 5.56/5.76 apply zenon_H120. apply sym_equal. exact zenon_H4f. % 5.56/5.76 apply (zenon_notand_s _ _ zenon_H15f); [ zenon_intro zenon_H7b | zenon_intro zenon_H160 ]. % 5.56/5.76 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.56/5.76 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e3) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H7b. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H7c. % 5.56/5.76 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.56/5.76 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 5.56/5.76 congruence. % 5.56/5.76 cut (((op (e0) (e0)) = (e3)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e3))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H7e. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_Hba. % 5.56/5.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.76 cut (((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 5.56/5.76 congruence. % 5.56/5.76 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.56/5.76 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H161. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H7c. % 5.56/5.76 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.56/5.76 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 5.56/5.76 congruence. % 5.56/5.76 apply (zenon_L157_); trivial. % 5.56/5.76 apply zenon_H7d. apply refl_equal. % 5.56/5.76 apply zenon_H7d. apply refl_equal. % 5.56/5.76 apply zenon_H6f. apply refl_equal. % 5.56/5.76 apply zenon_H7d. apply refl_equal. % 5.56/5.76 apply zenon_H7d. apply refl_equal. % 5.56/5.76 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H80 | zenon_intro zenon_H81 ]. % 5.56/5.76 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2))) = ((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H160. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H80. % 5.56/5.76 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 5.56/5.76 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 5.56/5.76 congruence. % 5.56/5.76 cut (((op (e3) (e2)) = (e1)) = ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (e1))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H162. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H15e. % 5.56/5.76 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.76 cut (((op (e3) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H83]. % 5.56/5.76 congruence. % 5.56/5.76 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H80 | zenon_intro zenon_H81 ]. % 5.56/5.76 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2))) = ((op (e3) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H83. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H80. % 5.56/5.76 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 5.56/5.76 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H84]. % 5.56/5.76 congruence. % 5.56/5.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.76 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 5.56/5.76 congruence. % 5.56/5.76 cut (((op (e0) (e0)) = (e3)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e3))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H7e. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_Hba. % 5.56/5.76 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.76 cut (((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H161]. % 5.56/5.76 congruence. % 5.56/5.76 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.56/5.76 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e0) (e0)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H161. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H7c. % 5.56/5.76 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.56/5.76 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 5.56/5.76 congruence. % 5.56/5.76 apply (zenon_L157_); trivial. % 5.56/5.76 apply zenon_H7d. apply refl_equal. % 5.56/5.76 apply zenon_H7d. apply refl_equal. % 5.56/5.76 apply zenon_H6f. apply refl_equal. % 5.56/5.76 apply zenon_H62. apply refl_equal. % 5.56/5.76 apply zenon_H81. apply refl_equal. % 5.56/5.76 apply zenon_H81. apply refl_equal. % 5.56/5.76 apply zenon_H94. apply refl_equal. % 5.56/5.76 apply zenon_H81. apply refl_equal. % 5.56/5.76 apply zenon_H81. apply refl_equal. % 5.56/5.76 (* end of lemma zenon_L158_ *) % 5.56/5.76 assert (zenon_L159_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H4a zenon_Hba zenon_H15e zenon_H77 zenon_H4c zenon_H4d. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 5.56/5.76 apply (zenon_L158_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H47 | zenon_intro zenon_H50 ]. % 5.56/5.76 exact (zenon_H77 zenon_H47). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 5.56/5.76 exact (zenon_H4c zenon_H52). % 5.56/5.76 exact (zenon_H4d zenon_H51). % 5.56/5.76 (* end of lemma zenon_L159_ *) % 5.56/5.76 assert (zenon_L160_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.76 do 0 intro. intros zenon_Hb7 zenon_H4d zenon_H4c zenon_H77 zenon_H4a zenon_H9f zenon_H41 zenon_H97 zenon_H163 zenon_H9d zenon_H42 zenon_H86 zenon_Hb0 zenon_H60 zenon_Hb4. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H149 | zenon_intro zenon_H164 ]. % 5.56/5.76 apply (zenon_L156_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H46 | zenon_intro zenon_H165 ]. % 5.56/5.76 apply (zenon_L38_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 5.56/5.76 exact (zenon_H77 zenon_H47). % 5.56/5.76 apply (zenon_L159_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.56/5.76 apply (zenon_L102_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.56/5.76 apply (zenon_L45_); trivial. % 5.56/5.76 apply (zenon_L46_); trivial. % 5.56/5.76 (* end of lemma zenon_L160_ *) % 5.56/5.76 assert (zenon_L161_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H3d zenon_H14a zenon_Hee. % 5.56/5.76 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H12c | zenon_intro zenon_H94 ]. % 5.56/5.76 cut (((e1) = (e1)) = ((e0) = (e1))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_Hee. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H12c. % 5.56/5.76 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.76 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 5.56/5.76 congruence. % 5.56/5.76 cut (((op (e0) (e3)) = (e0)) = ((e1) = (e0))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H12d. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H3d. % 5.56/5.76 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.76 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H166]. % 5.56/5.76 congruence. % 5.56/5.76 exact (zenon_H166 zenon_H14a). % 5.56/5.76 apply zenon_H67. apply refl_equal. % 5.56/5.76 apply zenon_H94. apply refl_equal. % 5.56/5.76 apply zenon_H94. apply refl_equal. % 5.56/5.76 (* end of lemma zenon_L161_ *) % 5.56/5.76 assert (zenon_L162_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H14f zenon_H150 zenon_Hb4 zenon_H60 zenon_H86 zenon_H9d zenon_H163 zenon_H41 zenon_H9f zenon_H4a zenon_H77 zenon_H4c zenon_H4d zenon_Hb7 zenon_Hb0 zenon_H97 zenon_H3d zenon_Hee. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.56/5.76 exact (zenon_H150 zenon_H152). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.56/5.76 apply (zenon_L160_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.56/5.76 apply (zenon_L156_); trivial. % 5.56/5.76 apply (zenon_L161_); trivial. % 5.56/5.76 (* end of lemma zenon_L162_ *) % 5.56/5.76 assert (zenon_L163_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H3d zenon_H167 zenon_H63. % 5.56/5.76 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.56/5.76 cut (((e2) = (e2)) = ((e0) = (e2))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H63. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H69. % 5.56/5.76 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.76 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 5.56/5.76 congruence. % 5.56/5.76 cut (((op (e0) (e3)) = (e0)) = ((e2) = (e0))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H6a. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H3d. % 5.56/5.76 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.76 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 5.56/5.76 congruence. % 5.56/5.76 exact (zenon_H168 zenon_H167). % 5.56/5.76 apply zenon_H67. apply refl_equal. % 5.56/5.76 apply zenon_H62. apply refl_equal. % 5.56/5.76 apply zenon_H62. apply refl_equal. % 5.56/5.76 (* end of lemma zenon_L163_ *) % 5.56/5.76 assert (zenon_L164_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H169 zenon_H16a zenon_H42 zenon_Hee zenon_H97 zenon_Hb7 zenon_H4d zenon_H4c zenon_H77 zenon_H4a zenon_H9f zenon_H41 zenon_H163 zenon_H9d zenon_H86 zenon_H60 zenon_Hb4 zenon_H150 zenon_H14f zenon_H3d zenon_H63. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.56/5.76 exact (zenon_H16a zenon_H16c). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.56/5.76 apply (zenon_L155_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.56/5.76 apply (zenon_L162_); trivial. % 5.56/5.76 apply (zenon_L163_); trivial. % 5.56/5.76 (* end of lemma zenon_L164_ *) % 5.56/5.76 assert (zenon_L165_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e2))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H16e zenon_H20 zenon_H6d zenon_Hb8 zenon_H169 zenon_H16a zenon_H42 zenon_Hee zenon_H97 zenon_Hb7 zenon_H4d zenon_H4c zenon_H77 zenon_H4a zenon_H9f zenon_H41 zenon_H163 zenon_H9d zenon_H86 zenon_H60 zenon_Hb4 zenon_H150 zenon_H14f zenon_H63. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.56/5.76 exact (zenon_H20 zenon_H1f). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.56/5.76 apply (zenon_L154_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.56/5.76 apply (zenon_L104_); trivial. % 5.56/5.76 apply (zenon_L164_); trivial. % 5.56/5.76 (* end of lemma zenon_L165_ *) % 5.56/5.76 assert (zenon_L166_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H171 zenon_Hee zenon_H3d zenon_H9a zenon_H3f zenon_H64 zenon_H97 zenon_H58. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H14a | zenon_intro zenon_H172 ]. % 5.56/5.76 apply (zenon_L161_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_H173 ]. % 5.56/5.76 apply (zenon_L34_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H144 | zenon_intro zenon_H5f ]. % 5.56/5.76 apply (zenon_L129_); trivial. % 5.56/5.76 exact (zenon_H58 zenon_H5f). % 5.56/5.76 (* end of lemma zenon_L166_ *) % 5.56/5.76 assert (zenon_L167_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((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)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H16e zenon_Hb4 zenon_H60 zenon_H6d zenon_H9d zenon_Hb8 zenon_Hb7 zenon_H171 zenon_Hee zenon_H9a zenon_H3f zenon_H64 zenon_H97 zenon_H58. % 5.56/5.76 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.76 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.56/5.76 exact (zenon_H20 zenon_H1f). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.56/5.76 apply (zenon_L154_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.56/5.76 apply (zenon_L104_); trivial. % 5.56/5.76 apply (zenon_L166_); trivial. % 5.56/5.76 (* end of lemma zenon_L167_ *) % 5.56/5.76 assert (zenon_L168_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e3) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.56/5.76 do 0 intro. intros zenon_H146 zenon_Hee zenon_Hce zenon_H60 zenon_H21 zenon_H13f zenon_H24 zenon_H124 zenon_H26 zenon_H9d zenon_Hd6 zenon_H6d zenon_H10d zenon_H77 zenon_H97 zenon_H64. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H12b | zenon_intro zenon_H147 ]. % 5.56/5.76 apply (zenon_L121_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H148 ]. % 5.56/5.76 apply (zenon_L125_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H47 | zenon_intro zenon_H144 ]. % 5.56/5.76 exact (zenon_H77 zenon_H47). % 5.56/5.76 apply (zenon_L129_); trivial. % 5.56/5.76 (* end of lemma zenon_L168_ *) % 5.56/5.76 assert (zenon_L169_ : (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H21 zenon_H13f zenon_H24 zenon_H15a zenon_H23 zenon_H26. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 5.56/5.76 exact (zenon_H13f zenon_H28). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 5.56/5.76 exact (zenon_H24 zenon_H2c). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 5.56/5.76 cut (((op (e0) (e1)) = (e2)) = ((op (e0) (e1)) = (op (e1) (e1)))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H23. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H15a. % 5.56/5.76 cut (((e2) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 5.56/5.76 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 5.56/5.76 congruence. % 5.56/5.76 apply zenon_H2a. apply refl_equal. % 5.56/5.76 apply zenon_H133. apply sym_equal. exact zenon_H2e. % 5.56/5.76 exact (zenon_H26 zenon_H2d). % 5.56/5.76 (* end of lemma zenon_L169_ *) % 5.56/5.76 assert (zenon_L170_ : ((op (e2) (e3)) = (e2)) -> ((op (e0) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H64 zenon_H167 zenon_H174. % 5.56/5.76 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H175 | zenon_intro zenon_H176 ]. % 5.56/5.76 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e0) (e3)) = (op (e2) (e3)))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H174. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H175. % 5.56/5.76 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 5.56/5.76 cut (((op (e2) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 5.56/5.76 congruence. % 5.56/5.76 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e0) (e3)))). % 5.56/5.76 intro zenon_D_pnotp. % 5.56/5.76 apply zenon_H177. % 5.56/5.76 rewrite <- zenon_D_pnotp. % 5.56/5.76 exact zenon_H64. % 5.56/5.76 cut (((e2) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 5.56/5.76 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 5.56/5.76 congruence. % 5.56/5.76 apply zenon_H176. apply refl_equal. % 5.56/5.76 apply zenon_H178. apply sym_equal. exact zenon_H167. % 5.56/5.76 apply zenon_H176. apply refl_equal. % 5.56/5.76 apply zenon_H176. apply refl_equal. % 5.56/5.76 (* end of lemma zenon_L170_ *) % 5.56/5.76 assert (zenon_L171_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e2)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H169 zenon_H16a zenon_H26 zenon_H23 zenon_H24 zenon_H13f zenon_H21 zenon_H149 zenon_H97 zenon_H64 zenon_H174. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.56/5.76 exact (zenon_H16a zenon_H16c). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.56/5.76 apply (zenon_L169_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.56/5.76 apply (zenon_L156_); trivial. % 5.56/5.76 apply (zenon_L170_); trivial. % 5.56/5.76 (* end of lemma zenon_L171_ *) % 5.56/5.76 assert (zenon_L172_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e2)) = (e1)) -> (((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 (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (((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 (e0) (e3)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 5.56/5.76 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_H57 zenon_H46 zenon_H8e zenon_H169 zenon_H16a zenon_H26 zenon_H23 zenon_H24 zenon_H21 zenon_H97 zenon_H64 zenon_H174 zenon_H146 zenon_Hce zenon_H60 zenon_H9d zenon_H6d zenon_H10d zenon_H77 zenon_H150 zenon_H14f zenon_H140 zenon_H3d zenon_Hed zenon_H13f zenon_Ha3 zenon_Hee zenon_H143. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.56/5.76 exact (zenon_H20 zenon_H1f). % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.56/5.76 apply (zenon_L36_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.56/5.76 exact (zenon_H150 zenon_H152). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.56/5.76 apply (zenon_L154_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.56/5.76 exact (zenon_H13f zenon_H28). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.56/5.76 apply (zenon_L122_); trivial. % 5.56/5.76 apply (zenon_L168_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.56/5.76 apply (zenon_L171_); trivial. % 5.56/5.76 apply (zenon_L161_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.56/5.76 apply (zenon_L66_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.56/5.76 exact (zenon_H13f zenon_H28). % 5.56/5.76 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.56/5.76 apply (zenon_L122_); trivial. % 5.56/5.76 apply (zenon_L127_); trivial. % 5.56/5.76 (* end of lemma zenon_L172_ *) % 5.56/5.76 assert (zenon_L173_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.56/5.76 do 0 intro. intros zenon_Hbc zenon_Hf0 zenon_H64. % 5.56/5.76 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.76 apply (zenon_L84_); trivial. % 5.56/5.76 (* end of lemma zenon_L173_ *) % 5.56/5.76 assert (zenon_L174_ : (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 5.56/5.76 do 0 intro. intros zenon_H16a zenon_H174 zenon_H169 zenon_H77 zenon_H13f zenon_H24 zenon_H16e zenon_H171 zenon_Hb8 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H8f zenon_H72 zenon_H86 zenon_H63 zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H158 zenon_H8e zenon_H60 zenon_H57 zenon_H9d zenon_H26 zenon_H6d zenon_H20 zenon_H179 zenon_H4b zenon_H45 zenon_H46 zenon_H4c zenon_H4a. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.76 apply (zenon_L11_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.76 apply (zenon_L16_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.76 apply (zenon_L37_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.76 apply (zenon_L153_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.76 apply (zenon_L32_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.76 apply (zenon_L167_); trivial. % 5.56/5.76 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.77 apply (zenon_L9_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.56/5.77 exact (zenon_H20 zenon_H1f). % 5.56/5.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.56/5.77 apply (zenon_L43_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.56/5.77 apply (zenon_L128_); trivial. % 5.56/5.77 apply (zenon_L172_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.77 apply (zenon_L44_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.77 apply (zenon_L173_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.77 apply (zenon_L138_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.77 apply (zenon_L51_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.77 apply (zenon_L52_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.77 apply (zenon_L53_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.77 apply (zenon_L54_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.77 apply (zenon_L56_); trivial. % 5.56/5.77 apply (zenon_L57_); trivial. % 5.56/5.77 apply (zenon_L42_); trivial. % 5.56/5.77 (* end of lemma zenon_L174_ *) % 5.56/5.77 assert (zenon_L175_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 5.56/5.77 do 0 intro. intros zenon_Hd7 zenon_H16a zenon_H174 zenon_H169 zenon_H77 zenon_H13f zenon_H24 zenon_H16e zenon_H171 zenon_Hb8 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H8f zenon_H72 zenon_H86 zenon_H63 zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H158 zenon_H8e zenon_H60 zenon_H57 zenon_H9d zenon_H26 zenon_H6d zenon_H20 zenon_H179 zenon_H4b zenon_H45 zenon_H4a. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.77 apply (zenon_L174_); trivial. % 5.56/5.77 (* end of lemma zenon_L175_ *) % 5.56/5.77 assert (zenon_L176_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H33 zenon_Hb0 zenon_H63. % 5.56/5.77 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.56/5.77 cut (((e2) = (e2)) = ((e0) = (e2))). % 5.56/5.77 intro zenon_D_pnotp. % 5.56/5.77 apply zenon_H63. % 5.56/5.77 rewrite <- zenon_D_pnotp. % 5.56/5.77 exact zenon_H69. % 5.56/5.77 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.56/5.77 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 5.56/5.77 congruence. % 5.56/5.77 cut (((op (e0) (e2)) = (e0)) = ((e2) = (e0))). % 5.56/5.77 intro zenon_D_pnotp. % 5.56/5.77 apply zenon_H6a. % 5.56/5.77 rewrite <- zenon_D_pnotp. % 5.56/5.77 exact zenon_H33. % 5.56/5.77 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.56/5.77 cut (((op (e0) (e2)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 5.56/5.77 congruence. % 5.56/5.77 exact (zenon_H17a zenon_Hb0). % 5.56/5.77 apply zenon_H67. apply refl_equal. % 5.56/5.77 apply zenon_H62. apply refl_equal. % 5.56/5.77 apply zenon_H62. apply refl_equal. % 5.56/5.77 (* end of lemma zenon_L176_ *) % 5.56/5.77 assert (zenon_L177_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e0)) = (e3)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H163 zenon_Hb0 zenon_H97 zenon_H9d zenon_H85 zenon_H4a zenon_Hba zenon_H77 zenon_H4c zenon_H4d. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H149 | zenon_intro zenon_H164 ]. % 5.56/5.77 apply (zenon_L156_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H46 | zenon_intro zenon_H165 ]. % 5.56/5.77 apply (zenon_L35_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 5.56/5.77 exact (zenon_H77 zenon_H47). % 5.56/5.77 apply (zenon_L159_); trivial. % 5.56/5.77 (* end of lemma zenon_L177_ *) % 5.56/5.77 assert (zenon_L178_ : (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e0)) -> ((op (e2) (e2)) = (e0)) -> False). % 5.56/5.77 do 0 intro. intros zenon_H45 zenon_H74 zenon_H4f. % 5.56/5.77 cut (((op (e1) (e2)) = (e0)) = ((op (e1) (e2)) = (op (e2) (e2)))). % 5.56/5.77 intro zenon_D_pnotp. % 5.56/5.77 apply zenon_H45. % 5.56/5.77 rewrite <- zenon_D_pnotp. % 5.56/5.77 exact zenon_H74. % 5.56/5.77 cut (((e0) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 5.56/5.77 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 5.56/5.77 congruence. % 5.56/5.77 apply zenon_H49. apply refl_equal. % 5.56/5.77 apply zenon_H120. apply sym_equal. exact zenon_H4f. % 5.56/5.77 (* end of lemma zenon_L178_ *) % 5.56/5.77 assert (zenon_L179_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e0)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H4a zenon_H74 zenon_H45 zenon_H77 zenon_H4c zenon_H4d. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 5.56/5.77 apply (zenon_L178_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H47 | zenon_intro zenon_H50 ]. % 5.56/5.77 exact (zenon_H77 zenon_H47). % 5.56/5.77 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 5.56/5.77 exact (zenon_H4c zenon_H52). % 5.56/5.77 exact (zenon_H4d zenon_H51). % 5.56/5.77 (* end of lemma zenon_L179_ *) % 5.56/5.77 assert (zenon_L180_ : (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e3)) = (e0)) -> False). % 5.56/5.77 do 0 intro. intros zenon_H14b zenon_H3d zenon_H56. % 5.56/5.77 cut (((op (e0) (e3)) = (e0)) = ((op (e0) (e3)) = (op (e1) (e3)))). % 5.56/5.77 intro zenon_D_pnotp. % 5.56/5.77 apply zenon_H14b. % 5.56/5.77 rewrite <- zenon_D_pnotp. % 5.56/5.77 exact zenon_H3d. % 5.56/5.77 cut (((e0) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 5.56/5.77 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 5.56/5.77 congruence. % 5.56/5.77 apply zenon_H17c. apply refl_equal. % 5.56/5.77 apply zenon_H17b. apply sym_equal. exact zenon_H56. % 5.56/5.77 (* end of lemma zenon_L180_ *) % 5.56/5.77 assert (zenon_L181_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (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 (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H14f zenon_H150 zenon_Hb4 zenon_H60 zenon_H86 zenon_H9d zenon_H17d zenon_H57 zenon_H163 zenon_H26 zenon_H6d zenon_H8e zenon_H13f zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H14b zenon_Hb7 zenon_Hb0 zenon_H97 zenon_H3d zenon_Hee. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.56/5.77 exact (zenon_H150 zenon_H152). % 5.56/5.77 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.56/5.77 apply (zenon_L19_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.56/5.77 exact (zenon_H26 zenon_H2d). % 5.56/5.77 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.56/5.77 apply (zenon_L177_); trivial. % 5.56/5.77 apply (zenon_L27_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.56/5.77 exact (zenon_H13f zenon_H28). % 5.56/5.77 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.56/5.77 apply (zenon_L179_); trivial. % 5.56/5.77 apply (zenon_L180_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.56/5.77 apply (zenon_L102_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.56/5.77 apply (zenon_L45_); trivial. % 5.56/5.77 apply (zenon_L46_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.56/5.77 apply (zenon_L156_); trivial. % 5.56/5.77 apply (zenon_L161_); trivial. % 5.56/5.77 (* end of lemma zenon_L181_ *) % 5.56/5.77 assert (zenon_L182_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (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 (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> False). % 5.56/5.77 do 0 intro. intros zenon_Hbc zenon_H16e zenon_Hb8 zenon_H63 zenon_H14f zenon_H150 zenon_Hb4 zenon_H60 zenon_H86 zenon_H9d zenon_H17d zenon_H57 zenon_H163 zenon_H26 zenon_H6d zenon_H8e zenon_H13f zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H14b zenon_Hb7 zenon_H97 zenon_Hee. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.56/5.77 exact (zenon_H20 zenon_H1f). % 5.56/5.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.56/5.77 apply (zenon_L47_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.56/5.77 apply (zenon_L176_); trivial. % 5.56/5.77 apply (zenon_L181_); trivial. % 5.56/5.77 (* end of lemma zenon_L182_ *) % 5.56/5.77 assert (zenon_L183_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> False). % 5.56/5.77 do 0 intro. intros zenon_Haa zenon_H9d zenon_H42 zenon_H26 zenon_H86 zenon_Hc2 zenon_H60 zenon_Ha7. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hab ]. % 5.56/5.77 apply (zenon_L102_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H2d | zenon_intro zenon_Hac ]. % 5.56/5.77 exact (zenon_H26 zenon_H2d). % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha6 ]. % 5.56/5.77 apply (zenon_L114_); trivial. % 5.56/5.77 apply (zenon_L42_); trivial. % 5.56/5.77 (* end of lemma zenon_L183_ *) % 5.56/5.77 assert (zenon_L184_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H14f zenon_H150 zenon_Ha7 zenon_H60 zenon_Hc2 zenon_H86 zenon_H26 zenon_H9d zenon_Haa zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H3d zenon_Hee. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.56/5.77 exact (zenon_H150 zenon_H152). % 5.56/5.77 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.56/5.77 apply (zenon_L183_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.56/5.77 apply (zenon_L133_); trivial. % 5.56/5.77 apply (zenon_L161_); trivial. % 5.56/5.77 (* end of lemma zenon_L184_ *) % 5.56/5.77 assert (zenon_L185_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H116 zenon_H129 zenon_H150 zenon_Haa zenon_H60 zenon_Ha7 zenon_Hc2 zenon_H86 zenon_H26 zenon_H9d zenon_H4a zenon_H4c zenon_H11f zenon_H4b zenon_Hee zenon_H3d zenon_H14f. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.77 apply (zenon_L184_); trivial. % 5.56/5.77 apply (zenon_L118_); trivial. % 5.56/5.77 (* end of lemma zenon_L185_ *) % 5.56/5.77 assert (zenon_L186_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((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) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H16e zenon_H25 zenon_H24 zenon_Hce zenon_H57 zenon_Hb4 zenon_H4d zenon_H155 zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H72 zenon_H8f zenon_H6d zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9f zenon_Hb7 zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_Hb8 zenon_H126 zenon_H123 zenon_H122 zenon_H12a zenon_H97 zenon_H14b zenon_Hf7 zenon_H116 zenon_H129 zenon_H150 zenon_Haa zenon_H60 zenon_Ha7 zenon_Hc2 zenon_H86 zenon_H26 zenon_H9d zenon_H4a zenon_H4c zenon_H11f zenon_H4b zenon_Hee zenon_H14f. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.56/5.77 exact (zenon_H20 zenon_H1f). % 5.56/5.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.56/5.77 apply (zenon_L2_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.56/5.77 apply (zenon_L145_); trivial. % 5.56/5.77 apply (zenon_L185_); trivial. % 5.56/5.77 (* end of lemma zenon_L186_ *) % 5.56/5.77 assert (zenon_L187_ : ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H52 zenon_Hb0 zenon_H11f. % 5.56/5.77 elim (classic ((op (e2) (e2)) = (op (e2) (e2)))); [ zenon_intro zenon_H101 | zenon_intro zenon_H102 ]. % 5.56/5.77 cut (((op (e2) (e2)) = (op (e2) (e2))) = ((op (e0) (e2)) = (op (e2) (e2)))). % 5.56/5.77 intro zenon_D_pnotp. % 5.56/5.77 apply zenon_H11f. % 5.56/5.77 rewrite <- zenon_D_pnotp. % 5.56/5.77 exact zenon_H101. % 5.56/5.77 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 5.56/5.77 cut (((op (e2) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 5.56/5.77 congruence. % 5.56/5.77 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e0) (e2)))). % 5.56/5.77 intro zenon_D_pnotp. % 5.56/5.77 apply zenon_H180. % 5.56/5.77 rewrite <- zenon_D_pnotp. % 5.56/5.77 exact zenon_H52. % 5.56/5.77 cut (((e2) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 5.56/5.77 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 5.56/5.77 congruence. % 5.56/5.77 apply zenon_H102. apply refl_equal. % 5.56/5.77 apply zenon_H181. apply sym_equal. exact zenon_Hb0. % 5.56/5.77 apply zenon_H102. apply refl_equal. % 5.56/5.77 apply zenon_H102. apply refl_equal. % 5.56/5.77 (* end of lemma zenon_L187_ *) % 5.56/5.77 assert (zenon_L188_ : (((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). % 5.56/5.77 do 0 intro. intros zenon_H169 zenon_H16a zenon_H97 zenon_H42 zenon_H11f zenon_H52 zenon_H3d zenon_H63. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.56/5.77 exact (zenon_H16a zenon_H16c). % 5.56/5.77 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.56/5.77 apply (zenon_L155_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.56/5.77 apply (zenon_L187_); trivial. % 5.56/5.77 apply (zenon_L163_); trivial. % 5.56/5.77 (* end of lemma zenon_L188_ *) % 5.56/5.77 assert (zenon_L189_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (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)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H3f zenon_H16e zenon_Hee zenon_Hb4 zenon_H60 zenon_H6d zenon_H9d zenon_Hb8 zenon_Hb7 zenon_H169 zenon_H16a zenon_H97 zenon_H11f zenon_H52 zenon_H63. % 5.56/5.77 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.77 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.56/5.77 exact (zenon_H20 zenon_H1f). % 5.56/5.77 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.56/5.77 apply (zenon_L154_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.56/5.77 apply (zenon_L104_); trivial. % 5.56/5.77 apply (zenon_L188_); trivial. % 5.56/5.77 (* end of lemma zenon_L189_ *) % 5.56/5.77 assert (zenon_L190_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> False). % 5.56/5.77 do 0 intro. intros zenon_Hbc zenon_H52 zenon_H11f. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.56/5.77 apply (zenon_L187_); trivial. % 5.56/5.77 (* end of lemma zenon_L190_ *) % 5.56/5.77 assert (zenon_L191_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((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)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (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) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.56/5.77 do 0 intro. intros zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H20 zenon_H8e zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H105 zenon_H9a zenon_H117 zenon_H9f zenon_Ha7 zenon_Haa zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H63 zenon_H97 zenon_H16a zenon_H169 zenon_Hb7 zenon_Hb8 zenon_H9d zenon_H6d zenon_Hee zenon_H16e zenon_H11f zenon_Hd9 zenon_Hb4 zenon_H57 zenon_H60 zenon_H52. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.77 apply (zenon_L16_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.77 apply (zenon_L97_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.77 apply (zenon_L58_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.77 apply (zenon_L32_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.77 apply (zenon_L189_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.77 apply (zenon_L9_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.77 apply (zenon_L59_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.77 apply (zenon_L44_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.77 apply (zenon_L190_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.77 apply (zenon_L61_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.77 apply (zenon_L62_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.77 apply (zenon_L52_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.77 apply (zenon_L53_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.77 apply (zenon_L54_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.77 apply (zenon_L63_); trivial. % 5.56/5.77 apply (zenon_L57_); trivial. % 5.56/5.77 (* end of lemma zenon_L191_ *) % 5.56/5.77 assert (zenon_L192_ : (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H25 zenon_H17d zenon_H174 zenon_H13f zenon_H171 zenon_H26 zenon_H179 zenon_H4b zenon_H24 zenon_H16e zenon_H16a zenon_H163 zenon_H169 zenon_Hb8 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H20. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.77 apply (zenon_L16_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.77 apply (zenon_L97_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.77 apply (zenon_L153_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.77 apply (zenon_L32_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.77 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.77 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.77 apply (zenon_L165_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.77 apply (zenon_L9_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.77 apply (zenon_L175_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.77 apply (zenon_L44_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.77 apply (zenon_L182_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.56/5.77 apply (zenon_L186_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.77 apply (zenon_L51_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.77 apply (zenon_L52_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.77 apply (zenon_L53_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.77 apply (zenon_L54_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.77 apply (zenon_L56_); trivial. % 5.56/5.77 apply (zenon_L57_); trivial. % 5.56/5.77 apply (zenon_L72_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.77 apply (zenon_L16_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.77 apply (zenon_L97_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.77 apply (zenon_L153_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.77 apply (zenon_L32_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.77 apply (zenon_L167_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.77 apply (zenon_L9_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.77 apply (zenon_L175_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.77 apply (zenon_L44_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.77 apply (zenon_L173_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.77 apply (zenon_L138_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.77 apply (zenon_L51_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.77 apply (zenon_L52_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.77 apply (zenon_L53_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.77 apply (zenon_L54_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.77 apply (zenon_L56_); trivial. % 5.56/5.77 apply (zenon_L57_); trivial. % 5.56/5.77 apply (zenon_L42_); trivial. % 5.56/5.77 apply (zenon_L191_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.77 apply (zenon_L186_); trivial. % 5.56/5.77 apply (zenon_L72_); trivial. % 5.56/5.77 apply (zenon_L118_); trivial. % 5.56/5.77 apply (zenon_L60_); trivial. % 5.56/5.77 (* end of lemma zenon_L192_ *) % 5.56/5.77 assert (zenon_L193_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e0)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> False). % 5.56/5.77 do 0 intro. intros zenon_H122 zenon_H41 zenon_H182. % 5.56/5.77 cut (((op (e1) (e0)) = (e1)) = ((op (e1) (e0)) = (op (e3) (e0)))). % 5.56/5.77 intro zenon_D_pnotp. % 5.56/5.77 apply zenon_H122. % 5.56/5.77 rewrite <- zenon_D_pnotp. % 5.56/5.77 exact zenon_H41. % 5.56/5.77 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 5.56/5.77 cut (((op (e1) (e0)) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 5.56/5.77 congruence. % 5.56/5.77 apply zenon_H9c. apply refl_equal. % 5.56/5.77 apply zenon_H183. apply sym_equal. exact zenon_H182. % 5.56/5.77 (* end of lemma zenon_L193_ *) % 5.56/5.77 assert (zenon_L194_ : (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 5.56/5.77 do 0 intro. intros zenon_H123 zenon_H42 zenon_Haf. % 5.56/5.77 cut (((op (e0) (e1)) = (e1)) = ((op (e0) (e1)) = (op (e3) (e1)))). % 5.56/5.77 intro zenon_D_pnotp. % 5.56/5.77 apply zenon_H123. % 5.56/5.77 rewrite <- zenon_D_pnotp. % 5.56/5.77 exact zenon_H42. % 5.56/5.77 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 5.56/5.77 cut (((op (e0) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 5.56/5.77 congruence. % 5.56/5.77 apply zenon_H2a. apply refl_equal. % 5.56/5.77 apply zenon_H184. apply sym_equal. exact zenon_Haf. % 5.56/5.77 (* end of lemma zenon_L194_ *) % 5.56/5.77 assert (zenon_L195_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H185 zenon_H41 zenon_H122 zenon_H42 zenon_H123 zenon_H4d zenon_H4c zenon_H77 zenon_Hba zenon_H4a zenon_H58. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H182 | zenon_intro zenon_H186 ]. % 5.56/5.77 apply (zenon_L193_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Haf | zenon_intro zenon_H187 ]. % 5.56/5.77 apply (zenon_L194_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H15e | zenon_intro zenon_H5f ]. % 5.56/5.77 apply (zenon_L159_); trivial. % 5.56/5.77 exact (zenon_H58 zenon_H5f). % 5.56/5.77 (* end of lemma zenon_L195_ *) % 5.56/5.77 assert (zenon_L196_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e3)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H10a zenon_H58 zenon_H4a zenon_H77 zenon_H4c zenon_H4d zenon_H123 zenon_H42 zenon_H122 zenon_H185 zenon_H9d zenon_H41 zenon_H6d zenon_Hd6 zenon_H60 zenon_Hfd. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.56/5.77 apply (zenon_L195_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.56/5.77 apply (zenon_L99_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.56/5.77 apply (zenon_L100_); trivial. % 5.56/5.77 apply (zenon_L72_); trivial. % 5.56/5.77 (* end of lemma zenon_L196_ *) % 5.56/5.77 assert (zenon_L197_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e0)) -> ((op (e0) (e0)) = (e3)) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H185 zenon_H41 zenon_H122 zenon_H42 zenon_H123 zenon_H4f zenon_Hba zenon_H58. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H182 | zenon_intro zenon_H186 ]. % 5.56/5.77 apply (zenon_L193_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Haf | zenon_intro zenon_H187 ]. % 5.56/5.77 apply (zenon_L194_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H15e | zenon_intro zenon_H5f ]. % 5.56/5.77 apply (zenon_L158_); trivial. % 5.56/5.77 exact (zenon_H58 zenon_H5f). % 5.56/5.77 (* end of lemma zenon_L197_ *) % 5.56/5.77 assert (zenon_L198_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.77 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_Hb7 zenon_H11f zenon_Hfd zenon_Hbe zenon_H86 zenon_H41 zenon_H9d zenon_H8f zenon_H6d zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H58 zenon_H123 zenon_H42 zenon_H122 zenon_H185 zenon_Hf3 zenon_H10a zenon_H60 zenon_Hb4. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.56/5.77 exact (zenon_H20 zenon_H1f). % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.56/5.77 apply (zenon_L195_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.56/5.77 apply (zenon_L19_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.56/5.77 apply (zenon_L78_); trivial. % 5.56/5.77 apply (zenon_L72_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.56/5.77 apply (zenon_L196_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H33 | zenon_intro zenon_H92 ]. % 5.56/5.77 apply (zenon_L98_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H74 | zenon_intro zenon_H93 ]. % 5.56/5.77 apply (zenon_L179_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H4f | zenon_intro zenon_H78 ]. % 5.56/5.77 apply (zenon_L197_); trivial. % 5.56/5.77 apply (zenon_L69_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.56/5.77 apply (zenon_L102_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H33 | zenon_intro zenon_H92 ]. % 5.56/5.77 apply (zenon_L103_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H74 | zenon_intro zenon_H93 ]. % 5.56/5.77 apply (zenon_L179_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H4f | zenon_intro zenon_H78 ]. % 5.56/5.77 apply (zenon_L197_); trivial. % 5.56/5.77 apply (zenon_L69_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.56/5.77 apply (zenon_L99_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.56/5.77 apply (zenon_L78_); trivial. % 5.56/5.77 apply (zenon_L72_); trivial. % 5.56/5.77 apply (zenon_L46_); trivial. % 5.56/5.77 (* end of lemma zenon_L198_ *) % 5.56/5.77 assert (zenon_L199_ : (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (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) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 5.56/5.77 do 0 intro. intros zenon_H77 zenon_H13f zenon_H169 zenon_H174 zenon_H16a zenon_H24 zenon_H3d zenon_H171 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H8f zenon_H72 zenon_H86 zenon_H63 zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H158 zenon_H8e zenon_H60 zenon_H57 zenon_H9d zenon_H26 zenon_H6d zenon_H20 zenon_H179 zenon_H4b zenon_H45 zenon_H46 zenon_H4c zenon_H4a. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.77 apply (zenon_L11_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.77 apply (zenon_L16_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.77 apply (zenon_L37_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.77 apply (zenon_L153_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.77 apply (zenon_L32_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.77 apply (zenon_L166_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.77 apply (zenon_L9_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.77 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.77 apply (zenon_L172_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.77 apply (zenon_L44_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.77 apply (zenon_L173_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.77 apply (zenon_L138_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.77 apply (zenon_L51_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.77 apply (zenon_L52_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.77 apply (zenon_L53_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.77 apply (zenon_L54_); trivial. % 5.56/5.77 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.77 apply (zenon_L56_); trivial. % 5.56/5.77 apply (zenon_L57_); trivial. % 5.56/5.77 apply (zenon_L42_); trivial. % 5.56/5.77 (* end of lemma zenon_L199_ *) % 5.56/5.77 assert (zenon_L200_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 5.56/5.78 do 0 intro. intros zenon_H3f zenon_H169 zenon_H16a zenon_H97 zenon_H11f zenon_H52 zenon_H3d zenon_H63. % 5.56/5.78 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.78 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.78 apply (zenon_L188_); trivial. % 5.56/5.78 (* end of lemma zenon_L200_ *) % 5.56/5.78 assert (zenon_L201_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((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 (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.56/5.78 do 0 intro. intros zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H20 zenon_H8e zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H105 zenon_H9a zenon_H117 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H63 zenon_H3d zenon_H97 zenon_H16a zenon_H169 zenon_H11f zenon_Hd9 zenon_Hb4 zenon_H57 zenon_H60 zenon_H52. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.78 apply (zenon_L16_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.78 apply (zenon_L97_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.78 apply (zenon_L58_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.78 apply (zenon_L32_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.78 apply (zenon_L200_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.78 apply (zenon_L9_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.78 apply (zenon_L59_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.78 apply (zenon_L44_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.78 apply (zenon_L190_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.78 apply (zenon_L61_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.78 apply (zenon_L62_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.78 apply (zenon_L52_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.78 apply (zenon_L53_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.78 apply (zenon_L54_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.78 apply (zenon_L63_); trivial. % 5.56/5.78 apply (zenon_L57_); trivial. % 5.56/5.78 (* end of lemma zenon_L201_ *) % 5.56/5.78 assert (zenon_L202_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 5.56/5.78 do 0 intro. intros zenon_H117 zenon_Hd9 zenon_H4a zenon_H46 zenon_H45 zenon_H4b zenon_H129 zenon_Hc2 zenon_H116. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.78 apply (zenon_L142_); trivial. % 5.56/5.78 apply (zenon_L60_); trivial. % 5.56/5.78 (* end of lemma zenon_L202_ *) % 5.56/5.78 assert (zenon_L203_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (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 (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 5.56/5.78 do 0 intro. intros zenon_Hbc zenon_H14f zenon_H150 zenon_Hb4 zenon_H60 zenon_H86 zenon_H9d zenon_H17d zenon_H57 zenon_H163 zenon_H26 zenon_H6d zenon_H8e zenon_H13f zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H14b zenon_Hb7 zenon_H97 zenon_H3d zenon_Hee. % 5.56/5.78 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.78 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.56/5.78 apply (zenon_L181_); trivial. % 5.56/5.78 (* end of lemma zenon_L203_ *) % 5.56/5.78 assert (zenon_L204_ : (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 5.56/5.78 do 0 intro. intros zenon_H20 zenon_H6d zenon_H26 zenon_H9d zenon_H46 zenon_H57 zenon_H60 zenon_H8e zenon_H158 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H86 zenon_H72 zenon_H8f zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H4a zenon_Hbe zenon_H163 zenon_H13f zenon_H3d zenon_H17d. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.78 apply (zenon_L16_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.78 apply (zenon_L37_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.78 apply (zenon_L153_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.78 apply (zenon_L32_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.78 apply (zenon_L39_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.78 apply (zenon_L9_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.78 apply (zenon_L81_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.78 apply (zenon_L44_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.78 apply (zenon_L203_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.78 apply (zenon_L83_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.78 apply (zenon_L51_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.78 apply (zenon_L52_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.78 apply (zenon_L53_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.78 apply (zenon_L54_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.78 apply (zenon_L56_); trivial. % 5.56/5.78 apply (zenon_L57_); trivial. % 5.56/5.78 apply (zenon_L84_); trivial. % 5.56/5.78 apply (zenon_L85_); trivial. % 5.56/5.78 apply (zenon_L82_); trivial. % 5.56/5.78 (* end of lemma zenon_L204_ *) % 5.56/5.78 assert (zenon_L205_ : (~((op (e1) (e1)) = (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) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((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)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 5.56/5.78 do 0 intro. intros zenon_H13f zenon_H169 zenon_H174 zenon_H16a zenon_H24 zenon_H3d zenon_H171 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H8f zenon_H72 zenon_H86 zenon_H63 zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H158 zenon_H8e zenon_H60 zenon_H57 zenon_H9d zenon_H6d zenon_H20 zenon_H179 zenon_H45 zenon_H46 zenon_H4a zenon_H163 zenon_H17d. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.78 apply (zenon_L199_); trivial. % 5.56/5.78 apply (zenon_L201_); trivial. % 5.56/5.78 apply (zenon_L202_); trivial. % 5.56/5.78 apply (zenon_L204_); trivial. % 5.56/5.78 apply (zenon_L64_); trivial. % 5.56/5.78 (* end of lemma zenon_L205_ *) % 5.56/5.78 assert (zenon_L206_ : (~((op (e0) (e3)) = (op (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) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (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)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (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) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 5.56/5.78 do 0 intro. intros zenon_Hb4 zenon_H60 zenon_H86 zenon_H9d zenon_H17d zenon_H163 zenon_H45 zenon_H179 zenon_H20 zenon_H6d zenon_H57 zenon_H8e zenon_H158 zenon_H11e zenon_H11a zenon_H118 zenon_H100 zenon_Hfd zenon_H63 zenon_H72 zenon_H8f zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H171 zenon_H24 zenon_H16a zenon_H174 zenon_H169 zenon_H13f zenon_H4a zenon_H77 zenon_H4c zenon_H4d zenon_Hb0 zenon_H97 zenon_H3d zenon_Hee. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.56/5.78 exact (zenon_H150 zenon_H152). % 5.56/5.78 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H149 | zenon_intro zenon_H164 ]. % 5.56/5.78 apply (zenon_L156_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H46 | zenon_intro zenon_H165 ]. % 5.56/5.78 apply (zenon_L205_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 5.56/5.78 exact (zenon_H77 zenon_H47). % 5.56/5.78 apply (zenon_L159_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.56/5.78 apply (zenon_L102_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.56/5.78 apply (zenon_L45_); trivial. % 5.56/5.78 apply (zenon_L46_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.56/5.78 apply (zenon_L156_); trivial. % 5.56/5.78 apply (zenon_L161_); trivial. % 5.56/5.78 (* end of lemma zenon_L206_ *) % 5.56/5.78 assert (zenon_L207_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e3)) = (op (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) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (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)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (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) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> False). % 5.56/5.78 do 0 intro. intros zenon_Hbc zenon_H16e zenon_Hb8 zenon_Hb4 zenon_H60 zenon_H86 zenon_H9d zenon_H17d zenon_H163 zenon_H45 zenon_H179 zenon_H6d zenon_H57 zenon_H8e zenon_H158 zenon_H11e zenon_H11a zenon_H118 zenon_H100 zenon_Hfd zenon_H63 zenon_H72 zenon_H8f zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H171 zenon_H24 zenon_H16a zenon_H174 zenon_H169 zenon_H13f zenon_H4a zenon_H77 zenon_H4c zenon_H4d zenon_H97 zenon_Hee. % 5.56/5.78 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.78 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.56/5.78 exact (zenon_H20 zenon_H1f). % 5.56/5.78 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.56/5.78 apply (zenon_L47_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.56/5.78 apply (zenon_L176_); trivial. % 5.56/5.78 apply (zenon_L206_); trivial. % 5.56/5.78 (* end of lemma zenon_L207_ *) % 5.56/5.78 assert (zenon_L208_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> False). % 5.56/5.78 do 0 intro. intros zenon_Hd7 zenon_Hdc zenon_H95. % 5.56/5.78 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.78 apply (zenon_L64_); trivial. % 5.56/5.78 (* end of lemma zenon_L208_ *) % 5.56/5.78 assert (zenon_L209_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((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)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 5.56/5.78 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_H3d zenon_H4a zenon_H4b zenon_H11f zenon_H4c zenon_H169 zenon_H16a zenon_H97 zenon_H57 zenon_H8f zenon_H8e zenon_H150 zenon_H14f zenon_Hce zenon_H60 zenon_H4d zenon_Hc2 zenon_H86 zenon_H6d zenon_H10d zenon_H17d zenon_H122 zenon_H13f zenon_H73 zenon_H63 zenon_Hee zenon_H95. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.56/5.78 exact (zenon_H20 zenon_H1f). % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.56/5.78 exact (zenon_H150 zenon_H152). % 5.56/5.78 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.56/5.78 exact (zenon_H16a zenon_H16c). % 5.56/5.78 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.56/5.78 apply (zenon_L155_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.56/5.78 apply (zenon_L19_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H33 | zenon_intro zenon_H92 ]. % 5.56/5.78 apply (zenon_L176_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H74 | zenon_intro zenon_H93 ]. % 5.56/5.78 apply (zenon_L21_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H4f | zenon_intro zenon_H78 ]. % 5.56/5.78 exact (zenon_H4b zenon_H4f). % 5.56/5.78 apply (zenon_L25_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.56/5.78 apply (zenon_L26_); trivial. % 5.56/5.78 apply (zenon_L27_); trivial. % 5.56/5.78 apply (zenon_L163_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.56/5.78 apply (zenon_L133_); trivial. % 5.56/5.78 apply (zenon_L161_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.56/5.78 apply (zenon_L140_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.56/5.78 apply (zenon_L112_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.56/5.78 exact (zenon_H13f zenon_H28). % 5.56/5.78 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.56/5.78 apply (zenon_L21_); trivial. % 5.56/5.78 apply (zenon_L67_); trivial. % 5.56/5.78 (* end of lemma zenon_L209_ *) % 5.56/5.78 assert (zenon_L210_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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 (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((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)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 5.56/5.78 do 0 intro. intros zenon_Hc0 zenon_H16e zenon_Hf7 zenon_H14b zenon_H12a zenon_H129 zenon_H123 zenon_H126 zenon_Hb8 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H110 zenon_H113 zenon_H116 zenon_Hf3 zenon_Hed zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H72 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H155 zenon_Hf6 zenon_H20 zenon_H4a zenon_H4b zenon_H11f zenon_H4c zenon_H169 zenon_H16a zenon_H97 zenon_H57 zenon_H8f zenon_H8e zenon_H150 zenon_H14f zenon_Hce zenon_H60 zenon_H4d zenon_H86 zenon_H6d zenon_H10d zenon_H17d zenon_H122 zenon_H13f zenon_H63 zenon_Hee zenon_H95. % 5.56/5.78 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.78 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.56/5.78 exact (zenon_H20 zenon_H1f). % 5.56/5.78 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.56/5.78 apply (zenon_L70_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.56/5.78 apply (zenon_L144_); trivial. % 5.56/5.78 apply (zenon_L209_); trivial. % 5.56/5.78 (* end of lemma zenon_L210_ *) % 5.56/5.78 assert (zenon_L211_ : (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (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) (e1)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> False). % 5.56/5.78 do 0 intro. intros zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H95 zenon_H24 zenon_Hb8 zenon_H77 zenon_H17d zenon_H163 zenon_H179 zenon_H171 zenon_H16a zenon_H174 zenon_H169 zenon_H13f zenon_H16e zenon_H4b. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.78 apply (zenon_L16_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.78 apply (zenon_L97_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.78 apply (zenon_L153_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.78 apply (zenon_L32_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.78 apply (zenon_L34_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.78 apply (zenon_L9_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.78 apply (zenon_L208_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.78 apply (zenon_L44_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.78 apply (zenon_L207_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.78 apply (zenon_L210_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.78 apply (zenon_L51_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.78 apply (zenon_L52_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.78 apply (zenon_L53_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.78 apply (zenon_L54_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.78 apply (zenon_L56_); trivial. % 5.56/5.78 apply (zenon_L57_); trivial. % 5.56/5.78 apply (zenon_L72_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.78 apply (zenon_L16_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.78 apply (zenon_L97_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.78 apply (zenon_L153_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.78 apply (zenon_L32_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.78 apply (zenon_L167_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.78 apply (zenon_L9_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.78 apply (zenon_L208_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.78 apply (zenon_L44_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.78 apply (zenon_L173_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.78 apply (zenon_L138_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.78 apply (zenon_L51_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.78 apply (zenon_L52_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.78 apply (zenon_L53_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.78 apply (zenon_L54_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.78 apply (zenon_L56_); trivial. % 5.56/5.78 apply (zenon_L57_); trivial. % 5.56/5.78 apply (zenon_L42_); trivial. % 5.56/5.78 apply (zenon_L191_); trivial. % 5.56/5.78 (* end of lemma zenon_L211_ *) % 5.56/5.78 assert (zenon_L212_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> False). % 5.56/5.78 do 0 intro. intros zenon_H4a zenon_H46 zenon_H45 zenon_H4b zenon_H179 zenon_H20 zenon_H6d zenon_H26 zenon_H9d zenon_H57 zenon_H60 zenon_H8e zenon_H158 zenon_H11e zenon_H11a zenon_H118 zenon_H100 zenon_Hfd zenon_H63 zenon_H86 zenon_H72 zenon_H8f zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_Hb8 zenon_H171 zenon_H16e zenon_H24 zenon_H13f zenon_H77 zenon_H169 zenon_H174 zenon_H16a. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.78 apply (zenon_L174_); trivial. % 5.56/5.78 apply (zenon_L191_); trivial. % 5.56/5.78 (* end of lemma zenon_L212_ *) % 5.56/5.78 assert (zenon_L213_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 5.56/5.78 do 0 intro. intros zenon_H179 zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H2c zenon_H77 zenon_H64 zenon_H146 zenon_Hb8 zenon_H171 zenon_H16e zenon_H129. % 5.56/5.78 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.78 apply (zenon_L16_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.78 apply (zenon_L97_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.78 apply (zenon_L147_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.78 apply (zenon_L32_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.78 apply (zenon_L167_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.78 apply (zenon_L90_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.78 apply (zenon_L92_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.78 apply (zenon_L44_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.78 apply (zenon_L173_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.78 apply (zenon_L138_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.78 apply (zenon_L51_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.78 apply (zenon_L52_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.78 apply (zenon_L53_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.78 apply (zenon_L54_); trivial. % 5.56/5.78 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.78 apply (zenon_L56_); trivial. % 5.56/5.78 apply (zenon_L57_); trivial. % 5.56/5.78 apply (zenon_L42_); trivial. % 5.56/5.78 (* end of lemma zenon_L213_ *) % 5.56/5.78 assert (zenon_L214_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (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) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.79 do 0 intro. intros zenon_H158 zenon_H20 zenon_H11e zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H57 zenon_H86 zenon_H72 zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb7 zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H4a zenon_H118 zenon_H11a zenon_H11f zenon_H52 zenon_Hb4 zenon_H2c zenon_Hce zenon_H60. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L87_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L89_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L90_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L92_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L190_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L93_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L62_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L94_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 (* end of lemma zenon_L214_ *) % 5.56/5.79 assert (zenon_L215_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (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) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> False). % 5.56/5.79 do 0 intro. intros zenon_H16e zenon_H77 zenon_H163 zenon_H26 zenon_H13f zenon_H17d zenon_Hb8 zenon_H4a zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H158 zenon_H2c zenon_H20 zenon_H179 zenon_H171. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L87_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L89_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L90_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L92_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L182_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L93_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L94_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L213_); trivial. % 5.56/5.79 apply (zenon_L214_); trivial. % 5.56/5.79 (* end of lemma zenon_L215_ *) % 5.56/5.79 assert (zenon_L216_ : (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e1)) = (e1)) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (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) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> False). % 5.56/5.79 do 0 intro. intros zenon_H4b zenon_H171 zenon_H179 zenon_H20 zenon_H2c zenon_H158 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H4a zenon_Hb8 zenon_H17d zenon_H13f zenon_H26 zenon_H163 zenon_H16e. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_L215_); trivial. % 5.56/5.79 apply (zenon_L150_); trivial. % 5.56/5.79 (* end of lemma zenon_L216_ *) % 5.56/5.79 assert (zenon_L217_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e3)) = (e1)) -> False). % 5.56/5.79 do 0 intro. intros zenon_H188 zenon_H2c zenon_H95. % 5.56/5.79 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e3)))). % 5.56/5.79 intro zenon_D_pnotp. % 5.56/5.79 apply zenon_H188. % 5.56/5.79 rewrite <- zenon_D_pnotp. % 5.56/5.79 exact zenon_H2c. % 5.56/5.79 cut (((e1) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 5.56/5.79 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 5.56/5.79 congruence. % 5.56/5.79 apply zenon_H11c. apply refl_equal. % 5.56/5.79 apply zenon_H9b. apply sym_equal. exact zenon_H95. % 5.56/5.79 (* end of lemma zenon_L217_ *) % 5.56/5.79 assert (zenon_L218_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> False). % 5.56/5.79 do 0 intro. intros zenon_Hbc zenon_H16e zenon_H6d zenon_Hb8 zenon_H63 zenon_H14f zenon_H150 zenon_Hb4 zenon_H60 zenon_H86 zenon_H9d zenon_H163 zenon_H41 zenon_H9f zenon_H4a zenon_H77 zenon_H4c zenon_H4d zenon_Hb7 zenon_H97 zenon_Hee. % 5.56/5.79 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.79 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.56/5.79 exact (zenon_H20 zenon_H1f). % 5.56/5.79 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.56/5.79 apply (zenon_L47_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.56/5.79 apply (zenon_L176_); trivial. % 5.56/5.79 apply (zenon_L162_); trivial. % 5.56/5.79 (* end of lemma zenon_L218_ *) % 5.56/5.79 assert (zenon_L219_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> False). % 5.56/5.79 do 0 intro. intros zenon_H117 zenon_Hd9 zenon_H100 zenon_Hfd zenon_H6d zenon_H126 zenon_H4b zenon_H4a zenon_H123 zenon_H122 zenon_H86 zenon_Hc2 zenon_Ha7 zenon_H60 zenon_Haa zenon_Hce zenon_H10d zenon_H9d zenon_H26 zenon_H45 zenon_H129 zenon_H116 zenon_H110 zenon_H41 zenon_H57 zenon_H8e zenon_Hb4 zenon_Hde. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L116_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L141_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.79 apply (zenon_L183_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L143_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L117_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L110_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L72_); trivial. % 5.56/5.79 apply (zenon_L118_); trivial. % 5.56/5.79 apply (zenon_L60_); trivial. % 5.56/5.79 (* end of lemma zenon_L219_ *) % 5.56/5.79 assert (zenon_L220_ : (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> False). % 5.56/5.79 do 0 intro. intros zenon_H4b zenon_H171 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14b zenon_H154 zenon_H155 zenon_H158 zenon_H179 zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_Hb8 zenon_H41 zenon_H169 zenon_H150 zenon_H163 zenon_H14f zenon_H16a zenon_H16e zenon_H26. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L97_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L101_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.79 apply (zenon_L165_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L106_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L218_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L110_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L97_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L167_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L106_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L173_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L138_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L42_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L97_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L101_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L189_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L106_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L190_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L110_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L62_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L219_); trivial. % 5.56/5.79 (* end of lemma zenon_L220_ *) % 5.56/5.79 assert (zenon_L221_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> False). % 5.56/5.79 do 0 intro. intros zenon_H3f zenon_Hf6 zenon_Hb7 zenon_H11f zenon_Hfd zenon_Hbe zenon_H86 zenon_H9d zenon_H8f zenon_H6d zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H58 zenon_H123 zenon_H122 zenon_H185 zenon_Hf3 zenon_H10a zenon_H60 zenon_Hb4. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.79 apply (zenon_L198_); trivial. % 5.56/5.79 (* end of lemma zenon_L221_ *) % 5.56/5.79 assert (zenon_L222_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 5.56/5.79 do 0 intro. intros zenon_H185 zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_Hb8 zenon_H169 zenon_H163 zenon_H16a zenon_H16e zenon_H179 zenon_H171 zenon_H174 zenon_H17d zenon_H188. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.79 apply (zenon_L192_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L79_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.79 apply (zenon_L198_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L81_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L207_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L83_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L42_); trivial. % 5.56/5.79 apply (zenon_L84_); trivial. % 5.56/5.79 apply (zenon_L85_); trivial. % 5.56/5.79 apply (zenon_L82_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_L211_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L116_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L141_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L34_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L143_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L117_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L210_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L72_); trivial. % 5.56/5.79 apply (zenon_L118_); trivial. % 5.56/5.79 apply (zenon_L60_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L79_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L34_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L81_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L207_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L83_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L84_); trivial. % 5.56/5.79 apply (zenon_L85_); trivial. % 5.56/5.79 apply (zenon_L82_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_L212_); trivial. % 5.56/5.79 apply (zenon_L202_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L79_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L39_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L81_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L182_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L83_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L84_); trivial. % 5.56/5.79 apply (zenon_L85_); trivial. % 5.56/5.79 apply (zenon_L82_); trivial. % 5.56/5.79 apply (zenon_L64_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.79 apply (zenon_L216_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L79_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L89_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L90_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L81_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L182_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L83_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L94_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L84_); trivial. % 5.56/5.79 apply (zenon_L85_); trivial. % 5.56/5.79 apply (zenon_L82_); trivial. % 5.56/5.79 apply (zenon_L217_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.79 apply (zenon_L220_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L79_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L101_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L221_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L81_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L218_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L83_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L42_); trivial. % 5.56/5.79 apply (zenon_L84_); trivial. % 5.56/5.79 apply (zenon_L85_); trivial. % 5.56/5.79 apply (zenon_L82_); trivial. % 5.56/5.79 apply (zenon_L33_); trivial. % 5.56/5.79 (* end of lemma zenon_L222_ *) % 5.56/5.79 assert (zenon_L223_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (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) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 5.56/5.79 do 0 intro. intros zenon_Hd7 zenon_H77 zenon_H13f zenon_H169 zenon_H174 zenon_H16a zenon_H24 zenon_H3d zenon_H171 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H8f zenon_H72 zenon_H86 zenon_H63 zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H158 zenon_H8e zenon_H60 zenon_H57 zenon_H9d zenon_H26 zenon_H6d zenon_H20 zenon_H179 zenon_H4b zenon_H45 zenon_H4a. % 5.56/5.79 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.79 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.79 apply (zenon_L199_); trivial. % 5.56/5.79 (* end of lemma zenon_L223_ *) % 5.56/5.79 assert (zenon_L224_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> False). % 5.56/5.79 do 0 intro. intros zenon_H17d zenon_H13f zenon_H174 zenon_H171 zenon_H26 zenon_H179 zenon_H4b zenon_H24 zenon_H169 zenon_H77 zenon_H163 zenon_H3d zenon_H16a zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H20. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L97_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.79 apply (zenon_L164_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L223_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L203_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.79 apply (zenon_L184_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L97_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L166_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L223_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L173_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L138_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L42_); trivial. % 5.56/5.79 apply (zenon_L201_); trivial. % 5.56/5.79 (* end of lemma zenon_L224_ *) % 5.56/5.79 assert (zenon_L225_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.79 do 0 intro. intros zenon_H158 zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H100 zenon_H63 zenon_H8e zenon_H72 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_Ha7 zenon_Haa zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hed zenon_H116 zenon_H113 zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H14b zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H129 zenon_H12a zenon_H10a zenon_Hf3 zenon_H185 zenon_H122 zenon_H123 zenon_H58 zenon_H45 zenon_H6d zenon_H8f zenon_Hfd zenon_H11f zenon_Hf6 zenon_H10d zenon_Hee zenon_H3d zenon_H97 zenon_Hb7 zenon_H4d zenon_H4c zenon_H77 zenon_H4a zenon_H9f zenon_H41 zenon_H163 zenon_H9d zenon_H86 zenon_H150 zenon_H14f zenon_Hbe zenon_H110 zenon_Hb4 zenon_H57 zenon_Hce zenon_H60. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L97_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L221_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L81_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.79 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.56/5.79 apply (zenon_L162_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L83_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 (* end of lemma zenon_L225_ *) % 5.56/5.79 assert (zenon_L226_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (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) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (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)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (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) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 5.56/5.79 do 0 intro. intros zenon_Hbc zenon_Hb4 zenon_H60 zenon_H86 zenon_H9d zenon_H17d zenon_H163 zenon_H45 zenon_H179 zenon_H6d zenon_H57 zenon_H8e zenon_H158 zenon_H11e zenon_H11a zenon_H118 zenon_H100 zenon_Hfd zenon_H63 zenon_H72 zenon_H8f zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H171 zenon_H24 zenon_H16a zenon_H174 zenon_H169 zenon_H13f zenon_H4a zenon_H77 zenon_H4c zenon_H4d zenon_H97 zenon_H3d zenon_Hee. % 5.56/5.79 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.79 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.56/5.79 apply (zenon_L206_); trivial. % 5.56/5.79 (* end of lemma zenon_L226_ *) % 5.56/5.79 assert (zenon_L227_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (e3)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> (~((e2) = (e3))) -> (~((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)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 5.56/5.79 do 0 intro. intros zenon_Hc0 zenon_Hf6 zenon_H20 zenon_H3d zenon_H4a zenon_H4b zenon_H11f zenon_H4c zenon_H169 zenon_H16a zenon_H97 zenon_H57 zenon_H8f zenon_H8e zenon_H150 zenon_H14f zenon_Hce zenon_H60 zenon_H4d zenon_H86 zenon_H6d zenon_H10d zenon_H17d zenon_H122 zenon_H13f zenon_H63 zenon_Hee zenon_H95. % 5.56/5.79 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.79 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.56/5.79 apply (zenon_L209_); trivial. % 5.56/5.79 (* end of lemma zenon_L227_ *) % 5.56/5.79 assert (zenon_L228_ : (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e0))) -> (((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))))) -> False). % 5.56/5.79 do 0 intro. intros zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H16a zenon_H3d zenon_H163 zenon_H169 zenon_H24 zenon_H179 zenon_H171 zenon_H174 zenon_H13f zenon_H17d zenon_H185. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_L224_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_L185_); trivial. % 5.56/5.79 apply (zenon_L60_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L97_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.79 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.79 apply (zenon_L225_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L81_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L226_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L83_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L42_); trivial. % 5.56/5.79 apply (zenon_L84_); trivial. % 5.56/5.79 apply (zenon_L85_); trivial. % 5.56/5.79 apply (zenon_L82_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L97_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L34_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L208_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L226_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L227_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L97_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L166_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L208_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L173_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L138_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L42_); trivial. % 5.56/5.79 apply (zenon_L201_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L116_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L141_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L34_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L143_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L117_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L227_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L72_); trivial. % 5.56/5.79 apply (zenon_L118_); trivial. % 5.56/5.79 apply (zenon_L60_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.79 apply (zenon_L16_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.79 apply (zenon_L97_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.79 apply (zenon_L153_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.79 apply (zenon_L32_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.79 apply (zenon_L34_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.79 apply (zenon_L9_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.79 apply (zenon_L208_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.79 apply (zenon_L44_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.79 apply (zenon_L226_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.79 apply (zenon_L83_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.79 apply (zenon_L51_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.79 apply (zenon_L52_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.79 apply (zenon_L53_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.79 apply (zenon_L54_); trivial. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.79 apply (zenon_L56_); trivial. % 5.56/5.79 apply (zenon_L57_); trivial. % 5.56/5.79 apply (zenon_L84_); trivial. % 5.56/5.79 apply (zenon_L85_); trivial. % 5.56/5.79 apply (zenon_L82_); trivial. % 5.56/5.79 (* end of lemma zenon_L228_ *) % 5.56/5.79 assert (zenon_L229_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e0) (e1)) = (op (e0) (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)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.79 do 0 intro. intros zenon_H158 zenon_H20 zenon_H11e zenon_H100 zenon_Hfd zenon_H63 zenon_H72 zenon_H8f zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9f zenon_Ha7 zenon_Haa zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H118 zenon_H11a zenon_Hee zenon_H3d zenon_H97 zenon_Hb7 zenon_H14b zenon_H4a zenon_H45 zenon_H77 zenon_H4c zenon_H4d zenon_H13f zenon_H8e zenon_H6d zenon_H26 zenon_H163 zenon_H57 zenon_H17d zenon_H9d zenon_H86 zenon_H150 zenon_H14f zenon_Hb4 zenon_H2c zenon_Hce zenon_H60. % 5.56/5.79 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.80 apply (zenon_L16_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.80 apply (zenon_L87_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.80 apply (zenon_L153_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.80 apply (zenon_L32_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.80 apply (zenon_L89_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.80 apply (zenon_L90_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.80 apply (zenon_L92_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.80 apply (zenon_L44_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.80 apply (zenon_L203_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.80 apply (zenon_L93_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.80 apply (zenon_L51_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.80 apply (zenon_L52_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.80 apply (zenon_L53_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.80 apply (zenon_L94_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.80 apply (zenon_L56_); trivial. % 5.56/5.80 apply (zenon_L57_); trivial. % 5.56/5.80 (* end of lemma zenon_L229_ *) % 5.56/5.80 assert (zenon_L230_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e2) (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) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> False). % 5.56/5.80 do 0 intro. intros zenon_H17d zenon_H3d zenon_H13f zenon_H26 zenon_H163 zenon_H77 zenon_H4a zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H158 zenon_H2c zenon_H20 zenon_H179 zenon_H171. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.80 apply (zenon_L229_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.80 apply (zenon_L16_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.80 apply (zenon_L97_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.80 apply (zenon_L147_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.80 apply (zenon_L32_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.80 apply (zenon_L166_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.80 apply (zenon_L90_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.80 apply (zenon_L92_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.80 apply (zenon_L44_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.80 apply (zenon_L173_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.80 apply (zenon_L138_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.80 apply (zenon_L51_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.80 apply (zenon_L52_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.80 apply (zenon_L53_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.80 apply (zenon_L54_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.80 apply (zenon_L56_); trivial. % 5.56/5.80 apply (zenon_L57_); trivial. % 5.56/5.80 apply (zenon_L42_); trivial. % 5.56/5.80 apply (zenon_L214_); trivial. % 5.56/5.80 (* end of lemma zenon_L230_ *) % 5.56/5.80 assert (zenon_L231_ : (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e1)) = (e1)) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (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 (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> False). % 5.56/5.80 do 0 intro. intros zenon_H4b zenon_H171 zenon_H179 zenon_H20 zenon_H2c zenon_H158 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H4a zenon_H163 zenon_H26 zenon_H13f zenon_H3d zenon_H17d. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.80 apply (zenon_L230_); trivial. % 5.56/5.80 apply (zenon_L150_); trivial. % 5.56/5.80 (* end of lemma zenon_L231_ *) % 5.56/5.80 assert (zenon_L232_ : ((op (e0) (e3)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 5.56/5.80 do 0 intro. intros zenon_H3d zenon_H163 zenon_H185 zenon_H41 zenon_Hbe zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H20 zenon_H179. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.80 apply (zenon_L225_); trivial. % 5.56/5.80 apply (zenon_L42_); trivial. % 5.56/5.80 apply (zenon_L84_); trivial. % 5.56/5.80 apply (zenon_L85_); trivial. % 5.56/5.80 apply (zenon_L82_); trivial. % 5.56/5.80 (* end of lemma zenon_L232_ *) % 5.56/5.80 assert (zenon_L233_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> False). % 5.56/5.80 do 0 intro. intros zenon_Hbc zenon_H3d zenon_H163 zenon_H185 zenon_H41 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H150 zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H57 zenon_H60 zenon_H8e zenon_H63 zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H179. % 5.56/5.80 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.80 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.56/5.80 apply (zenon_L232_); trivial. % 5.56/5.80 (* end of lemma zenon_L233_ *) % 5.56/5.80 assert (zenon_L234_ : (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e1) (e0)) = (e1)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> False). % 5.56/5.80 do 0 intro. intros zenon_H4b zenon_H171 zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H16a zenon_H3d zenon_H163 zenon_H41 zenon_H169 zenon_H179 zenon_H185 zenon_H26. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.80 apply (zenon_L16_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.80 apply (zenon_L97_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.80 apply (zenon_L153_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.80 apply (zenon_L32_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.80 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.56/5.80 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.56/5.80 apply (zenon_L164_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.80 apply (zenon_L9_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.80 apply (zenon_L106_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.80 apply (zenon_L44_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.80 apply (zenon_L233_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.80 apply (zenon_L110_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.80 apply (zenon_L51_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.80 apply (zenon_L52_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.80 apply (zenon_L53_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.80 apply (zenon_L54_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.80 apply (zenon_L56_); trivial. % 5.56/5.80 apply (zenon_L57_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.80 apply (zenon_L16_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.80 apply (zenon_L97_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.80 apply (zenon_L153_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.80 apply (zenon_L32_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.80 apply (zenon_L166_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.80 apply (zenon_L9_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.80 apply (zenon_L106_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.80 apply (zenon_L44_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.80 apply (zenon_L173_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.80 apply (zenon_L138_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.80 apply (zenon_L51_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.80 apply (zenon_L52_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.80 apply (zenon_L53_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.80 apply (zenon_L54_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.80 apply (zenon_L56_); trivial. % 5.56/5.80 apply (zenon_L57_); trivial. % 5.56/5.80 apply (zenon_L42_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.80 apply (zenon_L16_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.80 apply (zenon_L97_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.80 apply (zenon_L153_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.80 apply (zenon_L32_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.80 apply (zenon_L200_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.80 apply (zenon_L9_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.80 apply (zenon_L106_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.80 apply (zenon_L44_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.80 apply (zenon_L233_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.80 apply (zenon_L110_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.80 apply (zenon_L62_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.80 apply (zenon_L52_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.80 apply (zenon_L53_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.80 apply (zenon_L54_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.80 apply (zenon_L56_); trivial. % 5.56/5.80 apply (zenon_L57_); trivial. % 5.56/5.80 apply (zenon_L219_); trivial. % 5.56/5.80 (* end of lemma zenon_L234_ *) % 5.56/5.80 assert (zenon_L235_ : (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((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 (e1) (e1)) = (op (e1) (e3)))) -> False). % 5.56/5.80 do 0 intro. intros zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H16a zenon_H3d zenon_H163 zenon_H169 zenon_H179 zenon_H171 zenon_H174 zenon_H17d zenon_H185 zenon_H188. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.56/5.80 apply (zenon_L228_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.80 apply (zenon_L231_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.80 apply (zenon_L16_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.80 apply (zenon_L87_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.80 apply (zenon_L153_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.80 apply (zenon_L32_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.80 apply (zenon_L89_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.80 apply (zenon_L90_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.80 apply (zenon_L81_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.80 apply (zenon_L44_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.80 apply (zenon_L203_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.80 apply (zenon_L83_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.80 apply (zenon_L51_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.80 apply (zenon_L52_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.80 apply (zenon_L53_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.80 apply (zenon_L94_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.80 apply (zenon_L56_); trivial. % 5.56/5.80 apply (zenon_L57_); trivial. % 5.56/5.80 apply (zenon_L84_); trivial. % 5.56/5.80 apply (zenon_L85_); trivial. % 5.56/5.80 apply (zenon_L82_); trivial. % 5.56/5.80 apply (zenon_L217_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.80 apply (zenon_L234_); trivial. % 5.56/5.80 apply (zenon_L232_); trivial. % 5.56/5.80 apply (zenon_L33_); trivial. % 5.56/5.80 (* end of lemma zenon_L235_ *) % 5.56/5.80 assert (zenon_L236_ : ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 5.56/5.80 do 0 intro. intros zenon_H189 zenon_H185 zenon_H20 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H150 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H169 zenon_H163 zenon_H16e zenon_H179 zenon_H171 zenon_H174 zenon_H17d zenon_H188. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H189); [ zenon_intro zenon_H16a | zenon_intro zenon_H33 ]. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H3d ]. % 5.56/5.80 apply (zenon_L222_); trivial. % 5.56/5.80 apply (zenon_L235_); trivial. % 5.56/5.80 apply (zenon_L152_); trivial. % 5.56/5.80 (* end of lemma zenon_L236_ *) % 5.56/5.80 assert (zenon_L237_ : (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e0) (e1)) = (e0)) -> False). % 5.56/5.80 do 0 intro. intros zenon_H18a zenon_H1f zenon_H22. % 5.56/5.80 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e0) (e1)))). % 5.56/5.80 intro zenon_D_pnotp. % 5.56/5.80 apply zenon_H18a. % 5.56/5.80 rewrite <- zenon_D_pnotp. % 5.56/5.80 exact zenon_H1f. % 5.56/5.80 cut (((e0) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 5.56/5.80 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 5.56/5.80 congruence. % 5.56/5.80 apply zenon_H35. apply refl_equal. % 5.56/5.80 apply zenon_H18b. apply sym_equal. exact zenon_H22. % 5.56/5.80 (* end of lemma zenon_L237_ *) % 5.56/5.80 assert (zenon_L238_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> False). % 5.56/5.80 do 0 intro. intros zenon_H2f zenon_H18a zenon_H1f. % 5.56/5.80 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.56/5.80 apply (zenon_L237_); trivial. % 5.56/5.80 (* end of lemma zenon_L238_ *) % 5.56/5.80 assert (zenon_L239_ : (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e2) (e0)) = (e0)) -> False). % 5.56/5.80 do 0 intro. intros zenon_H18c zenon_H1f zenon_Hd6. % 5.56/5.80 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e2) (e0)))). % 5.56/5.80 intro zenon_D_pnotp. % 5.56/5.80 apply zenon_H18c. % 5.56/5.80 rewrite <- zenon_D_pnotp. % 5.56/5.80 exact zenon_H1f. % 5.56/5.80 cut (((e0) = (op (e2) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H18d]. % 5.56/5.80 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 5.56/5.80 congruence. % 5.56/5.80 apply zenon_H35. apply refl_equal. % 5.56/5.80 apply zenon_H18d. apply sym_equal. exact zenon_Hd6. % 5.56/5.80 (* end of lemma zenon_L239_ *) % 5.56/5.80 assert (zenon_L240_ : (((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)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.56/5.80 do 0 intro. intros zenon_H18e zenon_H1f zenon_H18c zenon_Ha3 zenon_Hee zenon_H4b zenon_H63 zenon_H64. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H18f ]. % 5.56/5.80 apply (zenon_L239_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H12f | zenon_intro zenon_H190 ]. % 5.56/5.80 apply (zenon_L122_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H4f | zenon_intro zenon_H65 ]. % 5.56/5.80 exact (zenon_H4b zenon_H4f). % 5.56/5.80 apply (zenon_L15_); trivial. % 5.56/5.80 (* end of lemma zenon_L240_ *) % 5.56/5.80 assert (zenon_L241_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (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)))) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.56/5.80 do 0 intro. intros zenon_Hd7 zenon_H18e zenon_H1f zenon_H18c zenon_Hee zenon_H4b zenon_H63 zenon_H64. % 5.56/5.80 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.80 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.80 apply (zenon_L240_); trivial. % 5.56/5.80 (* end of lemma zenon_L241_ *) % 5.56/5.80 assert (zenon_L242_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> False). % 5.56/5.80 do 0 intro. intros zenon_Hbc zenon_H1f. % 5.56/5.80 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.56/5.80 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.56/5.80 exact (zenon_H20 zenon_H1f). % 5.56/5.80 (* end of lemma zenon_L242_ *) % 5.56/5.80 assert (zenon_L243_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> False). % 5.56/5.80 do 0 intro. intros zenon_Hc8 zenon_H1f. % 5.56/5.80 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.56/5.80 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.56/5.80 exact (zenon_H20 zenon_H1f). % 5.56/5.80 (* end of lemma zenon_L243_ *) % 5.56/5.80 assert (zenon_L244_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 5.56/5.80 do 0 intro. intros zenon_H116 zenon_H1f zenon_H18a zenon_H32 zenon_H60 zenon_H18c zenon_Hee zenon_H63 zenon_H18e zenon_H97 zenon_H57 zenon_Hce zenon_Hde zenon_H4b zenon_H45 zenon_H46 zenon_H4c zenon_H4a. % 5.56/5.80 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.80 apply (zenon_L11_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.80 apply (zenon_L1_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.80 apply (zenon_L238_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.80 apply (zenon_L5_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.80 apply (zenon_L32_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.80 apply (zenon_L8_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.80 apply (zenon_L9_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.80 apply (zenon_L241_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.80 apply (zenon_L44_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.80 apply (zenon_L242_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.80 apply (zenon_L50_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.80 apply (zenon_L51_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.80 apply (zenon_L52_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.80 apply (zenon_L243_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.80 apply (zenon_L54_); trivial. % 5.56/5.80 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.80 apply (zenon_L56_); trivial. % 5.56/5.81 apply (zenon_L57_); trivial. % 5.56/5.81 (* end of lemma zenon_L244_ *) % 5.56/5.81 assert (zenon_L245_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> False). % 5.56/5.81 do 0 intro. intros zenon_Hd7 zenon_H116 zenon_H1f zenon_H18a zenon_H32 zenon_H60 zenon_H18c zenon_Hee zenon_H63 zenon_H18e zenon_H97 zenon_H57 zenon_Hce zenon_Hde zenon_H4b zenon_H45 zenon_H4a. % 5.56/5.81 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.56/5.81 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.56/5.81 apply (zenon_L244_); trivial. % 5.56/5.81 (* end of lemma zenon_L245_ *) % 5.56/5.81 assert (zenon_L246_ : (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e0)) = (e0)) -> False). % 5.56/5.81 do 0 intro. intros zenon_H191 zenon_H1f zenon_H31. % 5.56/5.81 cut (((op (e0) (e0)) = (e0)) = ((op (e0) (e0)) = (op (e1) (e0)))). % 5.56/5.81 intro zenon_D_pnotp. % 5.56/5.81 apply zenon_H191. % 5.56/5.81 rewrite <- zenon_D_pnotp. % 5.56/5.81 exact zenon_H1f. % 5.56/5.81 cut (((e0) = (op (e1) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 5.56/5.81 cut (((op (e0) (e0)) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 5.56/5.81 congruence. % 5.56/5.81 apply zenon_H35. apply refl_equal. % 5.56/5.81 apply zenon_H192. apply sym_equal. exact zenon_H31. % 5.56/5.81 (* end of lemma zenon_L246_ *) % 5.56/5.81 assert (zenon_L247_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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)))) -> (~((e2) = (e3))) -> (~((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 (e0) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.81 do 0 intro. intros zenon_Hde zenon_H18a zenon_H32 zenon_H9f zenon_H86 zenon_H26 zenon_H41 zenon_H9d zenon_H8e zenon_H1f zenon_H57 zenon_Hce zenon_H60. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.81 apply (zenon_L1_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.81 apply (zenon_L238_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.81 apply (zenon_L5_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.81 apply (zenon_L32_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.81 apply (zenon_L8_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.81 apply (zenon_L9_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.81 apply (zenon_L106_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.81 apply (zenon_L44_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.81 apply (zenon_L242_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.81 apply (zenon_L110_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.81 apply (zenon_L51_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.81 apply (zenon_L52_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.81 apply (zenon_L243_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.81 apply (zenon_L54_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.81 apply (zenon_L56_); trivial. % 5.56/5.81 apply (zenon_L57_); trivial. % 5.56/5.81 (* end of lemma zenon_L247_ *) % 5.56/5.81 assert (zenon_L248_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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)))) -> (~((e2) = (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (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))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.81 do 0 intro. intros zenon_H4a zenon_H45 zenon_H4b zenon_H18e zenon_H18c zenon_H116 zenon_Hee zenon_H97 zenon_Hde zenon_H18a zenon_H32 zenon_H9f zenon_H86 zenon_H26 zenon_H9d zenon_H8e zenon_H155 zenon_H63 zenon_H13f zenon_H191 zenon_H17d zenon_H1f zenon_H57 zenon_Hce zenon_H60. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.81 apply (zenon_L1_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.81 apply (zenon_L238_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.81 apply (zenon_L5_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.81 apply (zenon_L32_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.81 apply (zenon_L8_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.81 apply (zenon_L9_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.81 apply (zenon_L245_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.81 apply (zenon_L44_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.81 apply (zenon_L242_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.81 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.81 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.56/5.81 apply (zenon_L246_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.56/5.81 exact (zenon_H13f zenon_H28). % 5.56/5.81 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.56/5.81 apply (zenon_L21_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H41 | zenon_intro zenon_H156 ]. % 5.56/5.81 apply (zenon_L247_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H2c | zenon_intro zenon_H157 ]. % 5.56/5.81 exact (zenon_H24 zenon_H2c). % 5.56/5.81 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H46 | zenon_intro zenon_H95 ]. % 5.56/5.81 apply (zenon_L49_); trivial. % 5.56/5.81 apply (zenon_L67_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.81 apply (zenon_L51_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.81 apply (zenon_L52_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.81 apply (zenon_L243_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.81 apply (zenon_L54_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.81 apply (zenon_L56_); trivial. % 5.56/5.81 apply (zenon_L57_); trivial. % 5.56/5.81 (* end of lemma zenon_L248_ *) % 5.56/5.81 assert (zenon_L249_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.56/5.81 do 0 intro. intros zenon_Hde zenon_H18a zenon_Hd9 zenon_H1f zenon_H57 zenon_H60 zenon_H52. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.81 apply (zenon_L1_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.81 apply (zenon_L238_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.81 apply (zenon_L58_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.81 apply (zenon_L32_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.81 apply (zenon_L8_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.81 apply (zenon_L9_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.81 apply (zenon_L59_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.81 apply (zenon_L44_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.81 apply (zenon_L242_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.81 apply (zenon_L61_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.81 apply (zenon_L62_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.81 apply (zenon_L52_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.81 apply (zenon_L243_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.81 apply (zenon_L54_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.81 apply (zenon_L63_); trivial. % 5.56/5.81 apply (zenon_L57_); trivial. % 5.56/5.81 (* end of lemma zenon_L249_ *) % 5.56/5.81 assert (zenon_L250_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> (~((e1) = (e2))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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)))) -> (~((e2) = (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) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e0) = (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))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.81 do 0 intro. intros zenon_H4a zenon_H45 zenon_H4b zenon_H18e zenon_H18c zenon_H116 zenon_Hee zenon_H97 zenon_Hde zenon_H18a zenon_H32 zenon_H9f zenon_H86 zenon_H26 zenon_H9d zenon_H8e zenon_H155 zenon_H63 zenon_H13f zenon_H191 zenon_H17d zenon_H1f zenon_H57 zenon_Hce zenon_H60. % 5.56/5.81 apply (zenon_L248_); trivial. % 5.56/5.81 (* end of lemma zenon_L250_ *) % 5.56/5.81 assert (zenon_L251_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> False). % 5.56/5.81 do 0 intro. intros zenon_H116 zenon_Hf0 zenon_H1f zenon_H18a zenon_H32 zenon_H60 zenon_H86 zenon_Hbe zenon_H9d zenon_Hce zenon_H10d zenon_H110 zenon_H57 zenon_Hde. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.81 apply (zenon_L1_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.81 apply (zenon_L238_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.81 apply (zenon_L5_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.81 apply (zenon_L32_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.81 apply (zenon_L8_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.81 apply (zenon_L9_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.81 apply (zenon_L81_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.81 apply (zenon_L44_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.81 apply (zenon_L242_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.81 apply (zenon_L83_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.81 apply (zenon_L51_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.81 apply (zenon_L52_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.81 apply (zenon_L243_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.81 apply (zenon_L54_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.81 apply (zenon_L56_); trivial. % 5.56/5.81 apply (zenon_L57_); trivial. % 5.56/5.81 apply (zenon_L84_); trivial. % 5.56/5.81 (* end of lemma zenon_L251_ *) % 5.56/5.81 assert (zenon_L252_ : ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> False). % 5.56/5.81 do 0 intro. intros zenon_H116 zenon_Hf0 zenon_H1f zenon_H18a zenon_H32 zenon_H60 zenon_H86 zenon_Hbe zenon_H9d zenon_Hce zenon_H10d zenon_H110 zenon_H57 zenon_Hde. % 5.56/5.81 apply (zenon_L251_); trivial. % 5.56/5.81 (* end of lemma zenon_L252_ *) % 5.56/5.81 assert (zenon_L253_ : ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (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 (e1) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> False). % 5.56/5.81 do 0 intro. intros zenon_H115 zenon_Hf0 zenon_H10d zenon_H110 zenon_H17d zenon_H8e zenon_H86 zenon_H26 zenon_H9d zenon_H9f zenon_H155 zenon_H13f zenon_H191 zenon_H116 zenon_H18c zenon_Hee zenon_H63 zenon_H18e zenon_H97 zenon_H57 zenon_Hce zenon_Hde zenon_H45 zenon_H4a zenon_H60 zenon_H32 zenon_H18a zenon_H1f. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.81 apply (zenon_L250_); trivial. % 5.56/5.81 apply (zenon_L252_); trivial. % 5.56/5.81 (* end of lemma zenon_L253_ *) % 5.56/5.81 assert (zenon_L254_ : (((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)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 5.56/5.81 do 0 intro. intros zenon_H17d zenon_H1f zenon_H191 zenon_H13f zenon_H73 zenon_H63 zenon_Hee zenon_H95. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.56/5.81 apply (zenon_L246_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.56/5.81 exact (zenon_H13f zenon_H28). % 5.56/5.81 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.56/5.81 apply (zenon_L21_); trivial. % 5.56/5.81 apply (zenon_L67_); trivial. % 5.56/5.81 (* end of lemma zenon_L254_ *) % 5.56/5.81 assert (zenon_L255_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (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 (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> ((op (e1) (e3)) = (e1)) -> False). % 5.56/5.81 do 0 intro. intros zenon_Hc0 zenon_H17d zenon_H1f zenon_H191 zenon_H13f zenon_H63 zenon_Hee zenon_H95. % 5.56/5.81 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.56/5.81 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.56/5.81 apply (zenon_L254_); trivial. % 5.56/5.81 (* end of lemma zenon_L255_ *) % 5.56/5.81 assert (zenon_L256_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (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))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.81 do 0 intro. intros zenon_H4a zenon_H45 zenon_H4b zenon_Hde zenon_H97 zenon_H18e zenon_H18c zenon_H32 zenon_H18a zenon_H116 zenon_H95 zenon_Hee zenon_H63 zenon_H13f zenon_H191 zenon_H17d zenon_H1f zenon_H57 zenon_Hce zenon_H60. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.81 apply (zenon_L1_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.81 apply (zenon_L238_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.81 apply (zenon_L5_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.81 apply (zenon_L32_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.81 apply (zenon_L8_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.81 apply (zenon_L9_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.81 apply (zenon_L245_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.81 apply (zenon_L44_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.81 apply (zenon_L242_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.81 apply (zenon_L255_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.81 apply (zenon_L51_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.81 apply (zenon_L52_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.81 apply (zenon_L243_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.81 apply (zenon_L54_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.81 apply (zenon_L56_); trivial. % 5.56/5.81 apply (zenon_L57_); trivial. % 5.56/5.81 (* end of lemma zenon_L256_ *) % 5.56/5.81 assert (zenon_L257_ : (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (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))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.81 do 0 intro. intros zenon_H4a zenon_H45 zenon_H4b zenon_Hde zenon_H97 zenon_H18e zenon_H18c zenon_H32 zenon_H18a zenon_H116 zenon_H95 zenon_Hee zenon_H63 zenon_H13f zenon_H191 zenon_H17d zenon_H1f zenon_H57 zenon_Hce zenon_H60. % 5.56/5.81 apply (zenon_L256_); trivial. % 5.56/5.81 (* end of lemma zenon_L257_ *) % 5.56/5.81 assert (zenon_L258_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.81 do 0 intro. intros zenon_Hde zenon_H32 zenon_H11a zenon_H1f zenon_H2c zenon_Hce zenon_H60. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.81 apply (zenon_L1_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.81 apply (zenon_L87_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.81 apply (zenon_L5_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.81 apply (zenon_L32_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.81 apply (zenon_L8_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.81 apply (zenon_L90_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.81 apply (zenon_L92_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.81 apply (zenon_L44_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.81 apply (zenon_L242_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.81 apply (zenon_L93_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.81 apply (zenon_L51_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.81 apply (zenon_L52_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.81 apply (zenon_L243_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.81 apply (zenon_L94_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.81 apply (zenon_L56_); trivial. % 5.56/5.81 apply (zenon_L57_); trivial. % 5.56/5.81 (* end of lemma zenon_L258_ *) % 5.56/5.81 assert (zenon_L259_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> ((op (e3) (e3)) = (e3)) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.56/5.81 do 0 intro. intros zenon_Hde zenon_H60 zenon_H1f zenon_H2c zenon_H52. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.56/5.81 apply (zenon_L1_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.56/5.81 apply (zenon_L87_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.56/5.81 apply (zenon_L58_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.56/5.81 apply (zenon_L32_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.56/5.81 apply (zenon_L8_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.56/5.81 apply (zenon_L90_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.56/5.81 apply (zenon_L59_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.56/5.81 apply (zenon_L44_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.56/5.81 apply (zenon_L242_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.56/5.81 apply (zenon_L93_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.56/5.81 apply (zenon_L62_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.56/5.81 apply (zenon_L52_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.56/5.81 apply (zenon_L243_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.56/5.81 apply (zenon_L94_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.56/5.81 apply (zenon_L63_); trivial. % 5.56/5.81 apply (zenon_L57_); trivial. % 5.56/5.81 (* end of lemma zenon_L259_ *) % 5.56/5.81 assert (zenon_L260_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e3) (e3)) = (e3)) -> False). % 5.56/5.81 do 0 intro. intros zenon_Hde zenon_H32 zenon_H11a zenon_H1f zenon_H2c zenon_Hce zenon_H60. % 5.56/5.81 apply (zenon_L258_); trivial. % 5.56/5.81 (* end of lemma zenon_L260_ *) % 5.56/5.81 assert (zenon_L261_ : ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((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) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (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 (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 5.56/5.81 do 0 intro. intros zenon_Hdd zenon_H1f zenon_H18a zenon_H32 zenon_H60 zenon_H4a zenon_H45 zenon_Hde zenon_Hce zenon_H57 zenon_H97 zenon_H18e zenon_H63 zenon_Hee zenon_H18c zenon_H116 zenon_H191 zenon_H13f zenon_H155 zenon_H9f zenon_H9d zenon_H86 zenon_H8e zenon_H17d zenon_H110 zenon_H10d zenon_Hf0 zenon_H115. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.81 apply (zenon_L253_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.56/5.81 apply (zenon_L257_); trivial. % 5.56/5.81 apply (zenon_L252_); trivial. % 5.56/5.81 (* end of lemma zenon_L261_ *) % 5.56/5.81 assert (zenon_L262_ : ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e3) (e3)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (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 (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> False). % 5.56/5.81 do 0 intro. intros zenon_H158 zenon_H9a zenon_Hdd zenon_H1f zenon_H18a zenon_H32 zenon_H60 zenon_H4a zenon_H45 zenon_Hde zenon_Hce zenon_H57 zenon_H97 zenon_H18e zenon_H63 zenon_Hee zenon_H18c zenon_H116 zenon_H191 zenon_H155 zenon_H9f zenon_H9d zenon_H86 zenon_H8e zenon_H17d zenon_H110 zenon_H10d zenon_Hf0 zenon_H115. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.56/5.81 apply (zenon_L261_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.56/5.81 apply (zenon_L247_); trivial. % 5.56/5.81 apply (zenon_L33_); trivial. % 5.56/5.81 (* end of lemma zenon_L262_ *) % 5.56/5.81 assert (zenon_L263_ : ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e3) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> False). % 5.56/5.81 do 0 intro. intros zenon_H193 zenon_H191 zenon_H18c zenon_H18e zenon_H32 zenon_H18a zenon_H189 zenon_H185 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H63 zenon_H8e zenon_H60 zenon_H57 zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H169 zenon_H163 zenon_H16e zenon_H179 zenon_H171 zenon_H174 zenon_H17d zenon_H188 zenon_H194. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H150 | zenon_intro zenon_H22 ]. % 5.56/5.81 apply (zenon_L236_); trivial. % 5.56/5.81 apply (zenon_L96_); trivial. % 5.56/5.81 apply (zenon_L262_); trivial. % 5.56/5.81 (* end of lemma zenon_L263_ *) % 5.56/5.81 assert (zenon_L264_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 5.56/5.81 do 0 intro. intros zenon_H195 zenon_H194 zenon_H188 zenon_H17d zenon_H174 zenon_H171 zenon_H179 zenon_H16e zenon_H163 zenon_H169 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H8e zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H18a zenon_H32 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H53 zenon_H1f zenon_H55 zenon_H59 zenon_H58 zenon_H57 zenon_H63 zenon_H64 zenon_Hf7 zenon_Hf8. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H3d | zenon_intro zenon_Hfb ]. % 5.56/5.81 apply (zenon_L12_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H56 | zenon_intro zenon_Hfc ]. % 5.56/5.81 apply (zenon_L13_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H65 | zenon_intro zenon_H5b ]. % 5.56/5.81 apply (zenon_L15_); trivial. % 5.56/5.81 exact (zenon_Hf7 zenon_H5b). % 5.56/5.81 apply (zenon_L263_); trivial. % 5.56/5.81 (* end of lemma zenon_L264_ *) % 5.56/5.81 assert (zenon_L265_ : (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e0)) -> False). % 5.56/5.81 do 0 intro. intros zenon_Hee zenon_Haf zenon_H124. % 5.56/5.81 cut (((op (e3) (e1)) = (e1)) = ((e0) = (e1))). % 5.56/5.81 intro zenon_D_pnotp. % 5.56/5.81 apply zenon_Hee. % 5.56/5.81 rewrite <- zenon_D_pnotp. % 5.56/5.81 exact zenon_Haf. % 5.56/5.81 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.56/5.81 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 5.56/5.81 congruence. % 5.56/5.81 exact (zenon_H196 zenon_H124). % 5.56/5.81 apply zenon_H94. apply refl_equal. % 5.56/5.81 (* end of lemma zenon_L265_ *) % 5.56/5.81 assert (zenon_L266_ : (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e0)) -> False). % 5.56/5.81 do 0 intro. intros zenon_H6d zenon_Hd3 zenon_H78. % 5.56/5.81 cut (((op (e3) (e2)) = (e3)) = ((e0) = (e3))). % 5.56/5.81 intro zenon_D_pnotp. % 5.56/5.81 apply zenon_H6d. % 5.56/5.81 rewrite <- zenon_D_pnotp. % 5.56/5.81 exact zenon_Hd3. % 5.56/5.81 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.56/5.81 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 5.56/5.81 congruence. % 5.56/5.81 exact (zenon_H197 zenon_H78). % 5.56/5.81 apply zenon_H6f. apply refl_equal. % 5.56/5.81 (* end of lemma zenon_L266_ *) % 5.56/5.81 assert (zenon_L267_ : (((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)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 5.56/5.81 do 0 intro. intros zenon_H126 zenon_H1f zenon_H38 zenon_Haf zenon_Hee zenon_Hd3 zenon_H6d zenon_Hf7. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H39 | zenon_intro zenon_H127 ]. % 5.56/5.81 apply (zenon_L6_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H124 | zenon_intro zenon_H128 ]. % 5.56/5.81 apply (zenon_L265_); trivial. % 5.56/5.81 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H78 | zenon_intro zenon_H5b ]. % 5.56/5.81 apply (zenon_L266_); trivial. % 5.56/5.81 exact (zenon_Hf7 zenon_H5b). % 5.56/5.81 (* end of lemma zenon_L267_ *) % 5.56/5.81 assert (zenon_L268_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (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)))) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> False). % 5.56/5.81 do 0 intro. intros zenon_Had zenon_H126 zenon_H1f zenon_H38 zenon_Hee zenon_Hd3 zenon_H6d zenon_Hf7. % 5.56/5.81 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.56/5.81 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.56/5.81 apply (zenon_L267_); trivial. % 5.56/5.81 (* end of lemma zenon_L268_ *) % 5.56/5.81 assert (zenon_L269_ : ((op (e0) (e1)) = (e2)) -> ((op (e0) (e1)) = (e3)) -> (~((e2) = (e3))) -> False). % 5.56/5.81 do 0 intro. intros zenon_H15a zenon_Ha1 zenon_H86. % 5.56/5.81 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.56/5.81 cut (((e3) = (e3)) = ((e2) = (e3))). % 5.56/5.81 intro zenon_D_pnotp. % 5.56/5.81 apply zenon_H86. % 5.56/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_H6e. % 5.66/5.81 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.81 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 5.66/5.81 congruence. % 5.66/5.81 cut (((op (e0) (e1)) = (e2)) = ((e3) = (e2))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H87. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_H15a. % 5.66/5.81 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.81 cut (((op (e0) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 5.66/5.81 congruence. % 5.66/5.81 exact (zenon_Ha2 zenon_Ha1). % 5.66/5.81 apply zenon_H62. apply refl_equal. % 5.66/5.81 apply zenon_H6f. apply refl_equal. % 5.66/5.81 apply zenon_H6f. apply refl_equal. % 5.66/5.81 (* end of lemma zenon_L269_ *) % 5.66/5.81 assert (zenon_L270_ : ((op (e3) (e2)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> False). % 5.66/5.81 do 0 intro. intros zenon_Hd3 zenon_Hb1 zenon_H198. % 5.66/5.81 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H199 | zenon_intro zenon_H19a ]. % 5.66/5.81 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e0) (e2)) = (op (e3) (e2)))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H198. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_H199. % 5.66/5.81 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 5.66/5.81 cut (((op (e3) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19b]. % 5.66/5.81 congruence. % 5.66/5.81 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e0) (e2)))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H19b. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_Hd3. % 5.66/5.81 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 5.66/5.81 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 5.66/5.81 congruence. % 5.66/5.81 apply zenon_H19a. apply refl_equal. % 5.66/5.81 apply zenon_H19c. apply sym_equal. exact zenon_Hb1. % 5.66/5.81 apply zenon_H19a. apply refl_equal. % 5.66/5.81 apply zenon_H19a. apply refl_equal. % 5.66/5.81 (* end of lemma zenon_L270_ *) % 5.66/5.81 assert (zenon_L271_ : ((op (e0) (e3)) = (e0)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 5.66/5.81 do 0 intro. intros zenon_H3d zenon_Hb3 zenon_H6d. % 5.66/5.81 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.66/5.81 cut (((e3) = (e3)) = ((e0) = (e3))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H6d. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_H6e. % 5.66/5.81 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.81 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 5.66/5.81 congruence. % 5.66/5.81 cut (((op (e0) (e3)) = (e0)) = ((e3) = (e0))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H70. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_H3d. % 5.66/5.81 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.81 cut (((op (e0) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H19d]. % 5.66/5.81 congruence. % 5.66/5.81 exact (zenon_H19d zenon_Hb3). % 5.66/5.81 apply zenon_H67. apply refl_equal. % 5.66/5.81 apply zenon_H6f. apply refl_equal. % 5.66/5.81 apply zenon_H6f. apply refl_equal. % 5.66/5.81 (* end of lemma zenon_L271_ *) % 5.66/5.81 assert (zenon_L272_ : (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> False). % 5.66/5.81 do 0 intro. intros zenon_H9d zenon_Hb3 zenon_H14a. % 5.66/5.81 cut (((op (e0) (e3)) = (e3)) = ((e1) = (e3))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H9d. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_Hb3. % 5.66/5.81 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.81 cut (((op (e0) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H166]. % 5.66/5.81 congruence. % 5.66/5.81 exact (zenon_H166 zenon_H14a). % 5.66/5.81 apply zenon_H6f. apply refl_equal. % 5.66/5.81 (* end of lemma zenon_L272_ *) % 5.66/5.81 assert (zenon_L273_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e0)) -> (~((e0) = (e1))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.81 do 0 intro. intros zenon_H171 zenon_Hb3 zenon_H9d zenon_H56 zenon_Hee zenon_H64 zenon_H97 zenon_H58. % 5.66/5.81 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H14a | zenon_intro zenon_H172 ]. % 5.66/5.81 apply (zenon_L272_); trivial. % 5.66/5.81 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_H173 ]. % 5.66/5.81 apply (zenon_L67_); trivial. % 5.66/5.81 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H144 | zenon_intro zenon_H5f ]. % 5.66/5.81 apply (zenon_L129_); trivial. % 5.66/5.81 exact (zenon_H58 zenon_H5f). % 5.66/5.81 (* end of lemma zenon_L273_ *) % 5.66/5.81 assert (zenon_L274_ : (((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))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (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). % 5.66/5.81 do 0 intro. intros zenon_Hf8 zenon_H6d zenon_H58 zenon_H97 zenon_Hee zenon_H9d zenon_Hb3 zenon_H171 zenon_H64 zenon_H63 zenon_Hf7. % 5.66/5.81 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H3d | zenon_intro zenon_Hfb ]. % 5.66/5.81 apply (zenon_L271_); trivial. % 5.66/5.81 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H56 | zenon_intro zenon_Hfc ]. % 5.66/5.81 apply (zenon_L273_); trivial. % 5.66/5.81 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H65 | zenon_intro zenon_H5b ]. % 5.66/5.81 apply (zenon_L15_); trivial. % 5.66/5.81 exact (zenon_Hf7 zenon_H5b). % 5.66/5.81 (* end of lemma zenon_L274_ *) % 5.66/5.81 assert (zenon_L275_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (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))) -> (~((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). % 5.66/5.81 do 0 intro. intros zenon_Hb7 zenon_Hb8 zenon_H86 zenon_H15a zenon_H198 zenon_Hd3 zenon_Hf8 zenon_H6d zenon_H58 zenon_H97 zenon_Hee zenon_H9d zenon_H171 zenon_H64 zenon_H63 zenon_Hf7. % 5.66/5.81 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.81 exact (zenon_Hb8 zenon_Hba). % 5.66/5.81 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.81 apply (zenon_L269_); trivial. % 5.66/5.81 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.81 apply (zenon_L270_); trivial. % 5.66/5.81 apply (zenon_L274_); trivial. % 5.66/5.81 (* end of lemma zenon_L275_ *) % 5.66/5.81 assert (zenon_L276_ : (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e0) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 5.66/5.81 do 0 intro. intros zenon_H198 zenon_Hb0 zenon_Hc7. % 5.66/5.81 cut (((op (e0) (e2)) = (e2)) = ((op (e0) (e2)) = (op (e3) (e2)))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H198. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_Hb0. % 5.66/5.81 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 5.66/5.81 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 5.66/5.81 congruence. % 5.66/5.81 apply zenon_H121. apply refl_equal. % 5.66/5.81 apply zenon_H19e. apply sym_equal. exact zenon_Hc7. % 5.66/5.81 (* end of lemma zenon_L276_ *) % 5.66/5.81 assert (zenon_L277_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (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 (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 5.66/5.81 do 0 intro. intros zenon_Hc5 zenon_H169 zenon_H16a zenon_Hf7 zenon_H63 zenon_H171 zenon_H9d zenon_Hee zenon_H97 zenon_H58 zenon_H6d zenon_Hf8 zenon_Hd3 zenon_H86 zenon_Hb8 zenon_Hb7 zenon_H198 zenon_H174. % 5.66/5.81 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.81 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.66/5.81 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.81 exact (zenon_H16a zenon_H16c). % 5.66/5.81 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.81 apply (zenon_L275_); trivial. % 5.66/5.81 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.81 apply (zenon_L276_); trivial. % 5.66/5.81 apply (zenon_L170_); trivial. % 5.66/5.81 (* end of lemma zenon_L277_ *) % 5.66/5.81 assert (zenon_L278_ : (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 5.66/5.81 do 0 intro. intros zenon_Hf3 zenon_Hca zenon_Hd3. % 5.66/5.81 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e2)))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_Hf3. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_Hca. % 5.66/5.81 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 5.66/5.81 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 5.66/5.81 congruence. % 5.66/5.81 apply zenon_Hf5. apply refl_equal. % 5.66/5.81 apply zenon_H19f. apply sym_equal. exact zenon_Hd3. % 5.66/5.81 (* end of lemma zenon_L278_ *) % 5.66/5.81 assert (zenon_L279_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 5.66/5.81 do 0 intro. intros zenon_Hc8 zenon_Hf3 zenon_Hd3. % 5.66/5.81 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.66/5.81 apply (zenon_L278_); trivial. % 5.66/5.81 (* end of lemma zenon_L279_ *) % 5.66/5.81 assert (zenon_L280_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> False). % 5.66/5.81 do 0 intro. intros zenon_H1a0 zenon_Ha6 zenon_Hd3. % 5.66/5.81 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e3) (e2)))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H1a0. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_Ha6. % 5.66/5.81 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 5.66/5.81 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 5.66/5.81 congruence. % 5.66/5.81 apply zenon_H1a1. apply refl_equal. % 5.66/5.81 apply zenon_H19f. apply sym_equal. exact zenon_Hd3. % 5.66/5.81 (* end of lemma zenon_L280_ *) % 5.66/5.81 assert (zenon_L281_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 5.66/5.81 do 0 intro. intros zenon_Hcb zenon_H1a0 zenon_Hd3. % 5.66/5.81 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.81 apply (zenon_L280_); trivial. % 5.66/5.81 (* end of lemma zenon_L281_ *) % 5.66/5.81 assert (zenon_L282_ : ((op (e2) (e3)) = (e2)) -> ((op (e2) (e3)) = (e3)) -> (~((e2) = (e3))) -> False). % 5.66/5.81 do 0 intro. intros zenon_H64 zenon_Hcd zenon_H86. % 5.66/5.81 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.66/5.81 cut (((e3) = (e3)) = ((e2) = (e3))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H86. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_H6e. % 5.66/5.81 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.81 cut (((e3) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 5.66/5.81 congruence. % 5.66/5.81 cut (((op (e2) (e3)) = (e2)) = ((e3) = (e2))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H87. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_H64. % 5.66/5.81 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.81 cut (((op (e2) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 5.66/5.81 congruence. % 5.66/5.81 exact (zenon_H1a2 zenon_Hcd). % 5.66/5.81 apply zenon_H62. apply refl_equal. % 5.66/5.81 apply zenon_H6f. apply refl_equal. % 5.66/5.81 apply zenon_H6f. apply refl_equal. % 5.66/5.81 (* end of lemma zenon_L282_ *) % 5.66/5.81 assert (zenon_L283_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 5.66/5.81 do 0 intro. intros zenon_Hd1 zenon_H64 zenon_H86. % 5.66/5.81 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.66/5.81 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.66/5.81 apply (zenon_L282_); trivial. % 5.66/5.81 (* end of lemma zenon_L283_ *) % 5.66/5.81 assert (zenon_L284_ : (((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3))))) -> False). % 5.66/5.81 do 0 intro. intros zenon_Hd4. % 5.66/5.81 apply (zenon_and_s _ _ zenon_Hd4). zenon_intro zenon_H60. zenon_intro zenon_Hd5. % 5.66/5.81 apply (zenon_and_s _ _ zenon_Hd5). zenon_intro zenon_H60. zenon_intro zenon_H3e. % 5.66/5.81 exact (zenon_H3e zenon_H60). % 5.66/5.81 (* end of lemma zenon_L284_ *) % 5.66/5.81 assert (zenon_L285_ : ((op (e3) (e3)) = (e3)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e2)) = (op (e3) (e3)))) -> False). % 5.66/5.81 do 0 intro. intros zenon_H60 zenon_Hd3 zenon_H1a3. % 5.66/5.81 elim (classic ((op (e3) (e3)) = (op (e3) (e3)))); [ zenon_intro zenon_H8a | zenon_intro zenon_H8b ]. % 5.66/5.81 cut (((op (e3) (e3)) = (op (e3) (e3))) = ((op (e3) (e2)) = (op (e3) (e3)))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H1a3. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_H8a. % 5.66/5.81 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.66/5.81 cut (((op (e3) (e3)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a4]. % 5.66/5.81 congruence. % 5.66/5.81 cut (((op (e3) (e3)) = (e3)) = ((op (e3) (e3)) = (op (e3) (e2)))). % 5.66/5.81 intro zenon_D_pnotp. % 5.66/5.81 apply zenon_H1a4. % 5.66/5.81 rewrite <- zenon_D_pnotp. % 5.66/5.81 exact zenon_H60. % 5.66/5.81 cut (((e3) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 5.66/5.81 cut (((op (e3) (e3)) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 5.66/5.81 congruence. % 5.66/5.81 apply zenon_H8b. apply refl_equal. % 5.66/5.82 apply zenon_H19f. apply sym_equal. exact zenon_Hd3. % 5.66/5.82 apply zenon_H8b. apply refl_equal. % 5.66/5.82 apply zenon_H8b. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L285_ *) % 5.66/5.82 assert (zenon_L286_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H1a5 zenon_H1a0 zenon_Hb8 zenon_H198 zenon_H16a zenon_H4b zenon_H38 zenon_Hf8 zenon_Hf7 zenon_H64 zenon_H63 zenon_H57 zenon_H58 zenon_H55 zenon_H1f zenon_H53 zenon_H193 zenon_H191 zenon_H18c zenon_H18e zenon_H32 zenon_H18a zenon_H189 zenon_H185 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H8e zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H169 zenon_H163 zenon_H16e zenon_H179 zenon_H171 zenon_H174 zenon_H17d zenon_H188 zenon_H194 zenon_H195. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.82 apply (zenon_L264_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.82 apply (zenon_L1_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.82 apply (zenon_L238_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.82 apply (zenon_L5_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.82 apply (zenon_L7_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.82 apply (zenon_L8_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.82 apply (zenon_L9_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.82 apply (zenon_L241_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.82 apply (zenon_L268_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.82 apply (zenon_L173_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.82 apply (zenon_L138_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.82 apply (zenon_L51_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.82 apply (zenon_L277_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.82 apply (zenon_L279_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.82 apply (zenon_L281_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.82 apply (zenon_L283_); trivial. % 5.66/5.82 apply (zenon_L284_); trivial. % 5.66/5.82 (* end of lemma zenon_L286_ *) % 5.66/5.82 assert (zenon_L287_ : (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e0)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H6d zenon_Ha6 zenon_H124. % 5.66/5.82 cut (((op (e3) (e1)) = (e3)) = ((e0) = (e3))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H6d. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Ha6. % 5.66/5.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.82 cut (((op (e3) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H196 zenon_H124). % 5.66/5.82 apply zenon_H6f. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L287_ *) % 5.66/5.82 assert (zenon_L288_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H140 zenon_H42 zenon_H13f zenon_Ha3 zenon_Hee zenon_H6d zenon_Ha6. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.66/5.82 apply (zenon_L154_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.66/5.82 exact (zenon_H13f zenon_H28). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.66/5.82 apply (zenon_L122_); trivial. % 5.66/5.82 apply (zenon_L287_); trivial. % 5.66/5.82 (* end of lemma zenon_L288_ *) % 5.66/5.82 assert (zenon_L289_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Haa zenon_H26 zenon_H9d zenon_H140 zenon_H42 zenon_H13f zenon_Ha3 zenon_Hee zenon_H6d. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hab ]. % 5.66/5.82 apply (zenon_L102_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H2d | zenon_intro zenon_Hac ]. % 5.66/5.82 exact (zenon_H26 zenon_H2d). % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha6 ]. % 5.66/5.82 apply (zenon_L41_); trivial. % 5.66/5.82 apply (zenon_L288_); trivial. % 5.66/5.82 (* end of lemma zenon_L289_ *) % 5.66/5.82 assert (zenon_L290_ : ((op (e1) (e2)) = (e1)) -> ((op (e0) (e2)) = (e1)) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H46 zenon_H149 zenon_H1a6. % 5.66/5.82 elim (classic ((op (e1) (e2)) = (op (e1) (e2)))); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H49 ]. % 5.66/5.82 cut (((op (e1) (e2)) = (op (e1) (e2))) = ((op (e0) (e2)) = (op (e1) (e2)))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1a6. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H1a7. % 5.66/5.82 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 5.66/5.82 cut (((op (e1) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 5.66/5.82 congruence. % 5.66/5.82 cut (((op (e1) (e2)) = (e1)) = ((op (e1) (e2)) = (op (e0) (e2)))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1a8. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H46. % 5.66/5.82 cut (((e1) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 5.66/5.82 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 5.66/5.82 congruence. % 5.66/5.82 apply zenon_H49. apply refl_equal. % 5.66/5.82 apply zenon_H1a9. apply sym_equal. exact zenon_H149. % 5.66/5.82 apply zenon_H49. apply refl_equal. % 5.66/5.82 apply zenon_H49. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L290_ *) % 5.66/5.82 assert (zenon_L291_ : (~((op (e0) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e1)) -> ((op (e3) (e3)) = (e1)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hb4 zenon_H14a zenon_H5f. % 5.66/5.82 cut (((op (e0) (e3)) = (e1)) = ((op (e0) (e3)) = (op (e3) (e3)))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_Hb4. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H14a. % 5.66/5.82 cut (((e1) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 5.66/5.82 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 5.66/5.82 congruence. % 5.66/5.82 apply zenon_H17c. apply refl_equal. % 5.66/5.82 apply zenon_H1aa. apply sym_equal. exact zenon_H5f. % 5.66/5.82 (* end of lemma zenon_L291_ *) % 5.66/5.82 assert (zenon_L292_ : (((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 (e3) (e3)) = (e3))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H55 zenon_Hf7 zenon_H14a zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 5.66/5.82 exact (zenon_Hf7 zenon_H5b). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 5.66/5.82 apply (zenon_L291_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 5.66/5.82 exact (zenon_H59 zenon_H61). % 5.66/5.82 exact (zenon_H3e zenon_H60). % 5.66/5.82 (* end of lemma zenon_L292_ *) % 5.66/5.82 assert (zenon_L293_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((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 (e3) (e3)) = (e3))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hd7 zenon_H14f zenon_H150 zenon_H6d zenon_Hee zenon_H13f zenon_H140 zenon_H9d zenon_H26 zenon_Haa zenon_H1a6 zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.82 exact (zenon_H150 zenon_H152). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.82 apply (zenon_L289_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.82 apply (zenon_L290_); trivial. % 5.66/5.82 apply (zenon_L292_); trivial. % 5.66/5.82 (* end of lemma zenon_L293_ *) % 5.66/5.82 assert (zenon_L294_ : (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e1)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H9d zenon_Ha6 zenon_Haf. % 5.66/5.82 cut (((op (e3) (e1)) = (e3)) = ((e1) = (e3))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H9d. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Ha6. % 5.66/5.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.82 cut (((op (e3) (e1)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H1ab zenon_Haf). % 5.66/5.82 apply zenon_H6f. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L294_ *) % 5.66/5.82 assert (zenon_L295_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Had zenon_H9d zenon_Ha6. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.66/5.82 apply (zenon_L294_); trivial. % 5.66/5.82 (* end of lemma zenon_L295_ *) % 5.66/5.82 assert (zenon_L296_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H169 zenon_H16a zenon_H26 zenon_H23 zenon_H24 zenon_H13f zenon_H21 zenon_Hc7 zenon_H198 zenon_H64 zenon_H174. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.82 exact (zenon_H16a zenon_H16c). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.82 apply (zenon_L169_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.82 apply (zenon_L276_); trivial. % 5.66/5.82 apply (zenon_L170_); trivial. % 5.66/5.82 (* end of lemma zenon_L296_ *) % 5.66/5.82 assert (zenon_L297_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hc5 zenon_H169 zenon_H16a zenon_H26 zenon_H23 zenon_H24 zenon_H13f zenon_H21 zenon_H198 zenon_H174. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.66/5.82 apply (zenon_L296_); trivial. % 5.66/5.82 (* end of lemma zenon_L297_ *) % 5.66/5.82 assert (zenon_L298_ : (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H143 zenon_Hca zenon_Ha6. % 5.66/5.82 cut (((op (e3) (e0)) = (e3)) = ((op (e3) (e0)) = (op (e3) (e1)))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H143. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Hca. % 5.66/5.82 cut (((e3) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 5.66/5.82 cut (((op (e3) (e0)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 5.66/5.82 congruence. % 5.66/5.82 apply zenon_Hf5. apply refl_equal. % 5.66/5.82 apply zenon_Ha9. apply sym_equal. exact zenon_Ha6. % 5.66/5.82 (* end of lemma zenon_L298_ *) % 5.66/5.82 assert (zenon_L299_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hc8 zenon_H143 zenon_Ha6. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.66/5.82 apply (zenon_L298_); trivial. % 5.66/5.82 (* end of lemma zenon_L299_ *) % 5.66/5.82 assert (zenon_L300_ : (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hee zenon_H46 zenon_H74. % 5.66/5.82 cut (((op (e1) (e2)) = (e1)) = ((e0) = (e1))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_Hee. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H46. % 5.66/5.82 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.82 cut (((op (e1) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H75 zenon_H74). % 5.66/5.82 apply zenon_H94. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L300_ *) % 5.66/5.82 assert (zenon_L301_ : (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H6d zenon_H89 zenon_H56. % 5.66/5.82 cut (((op (e1) (e3)) = (e3)) = ((e0) = (e3))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H6d. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H89. % 5.66/5.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.82 cut (((op (e1) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_Hef zenon_H56). % 5.66/5.82 apply zenon_H6f. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L301_ *) % 5.66/5.82 assert (zenon_L302_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (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 (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hcb zenon_H17d zenon_H1f zenon_H191 zenon_H13f zenon_H46 zenon_Hee zenon_H6d. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.82 apply (zenon_L246_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.82 exact (zenon_H13f zenon_H28). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.82 apply (zenon_L300_); trivial. % 5.66/5.82 apply (zenon_L301_); trivial. % 5.66/5.82 (* end of lemma zenon_L302_ *) % 5.66/5.82 assert (zenon_L303_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hd1 zenon_H1a0 zenon_Ha6. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.66/5.82 apply (zenon_L280_); trivial. % 5.66/5.82 (* end of lemma zenon_L303_ *) % 5.66/5.82 assert (zenon_L304_ : (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H6d zenon_Hca zenon_H39. % 5.66/5.82 cut (((op (e3) (e0)) = (e3)) = ((e0) = (e3))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H6d. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Hca. % 5.66/5.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.82 cut (((op (e3) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H1ac zenon_H39). % 5.66/5.82 apply zenon_H6f. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L304_ *) % 5.66/5.82 assert (zenon_L305_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H3b zenon_H6d zenon_Hca. % 5.66/5.82 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.66/5.82 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.66/5.82 apply (zenon_L304_); trivial. % 5.66/5.82 (* end of lemma zenon_L305_ *) % 5.66/5.82 assert (zenon_L306_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((op (e1) (e2)) = (e1)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Had zenon_Hdc zenon_H46. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.66/5.82 apply (zenon_L64_); trivial. % 5.66/5.82 (* end of lemma zenon_L306_ *) % 5.66/5.82 assert (zenon_L307_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hcb zenon_H143 zenon_Hca. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.82 apply (zenon_L298_); trivial. % 5.66/5.82 (* end of lemma zenon_L307_ *) % 5.66/5.82 assert (zenon_L308_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hd1 zenon_Hf3 zenon_Hca. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.66/5.82 apply (zenon_L278_); trivial. % 5.66/5.82 (* end of lemma zenon_L308_ *) % 5.66/5.82 assert (zenon_L309_ : (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e2) (e3)) = (e2)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H1ad zenon_H52 zenon_H64. % 5.66/5.82 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e2) (e3)))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1ad. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H52. % 5.66/5.82 cut (((e2) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 5.66/5.82 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 5.66/5.82 congruence. % 5.66/5.82 apply zenon_H102. apply refl_equal. % 5.66/5.82 apply zenon_H112. apply sym_equal. exact zenon_H64. % 5.66/5.82 (* end of lemma zenon_L309_ *) % 5.66/5.82 assert (zenon_L310_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hc5 zenon_H1ad zenon_H52. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.82 apply (zenon_L309_); trivial. % 5.66/5.82 (* end of lemma zenon_L310_ *) % 5.66/5.82 assert (zenon_L311_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (~((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 (e2) (e2)) = (e2)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hde zenon_H18a zenon_H38 zenon_Hdc zenon_H11f zenon_Hd9 zenon_H1ad zenon_H6d zenon_Hee zenon_H46 zenon_H13f zenon_H191 zenon_H1f zenon_H17d zenon_H52. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.82 apply (zenon_L1_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.82 apply (zenon_L238_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.82 apply (zenon_L58_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.82 apply (zenon_L7_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.82 apply (zenon_L8_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.82 apply (zenon_L9_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.82 apply (zenon_L59_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.82 apply (zenon_L306_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.82 apply (zenon_L190_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.82 apply (zenon_L61_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.82 apply (zenon_L62_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.82 apply (zenon_L310_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.82 apply (zenon_L243_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.82 apply (zenon_L302_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.82 apply (zenon_L63_); trivial. % 5.66/5.82 apply (zenon_L284_); trivial. % 5.66/5.82 (* end of lemma zenon_L311_ *) % 5.66/5.82 assert (zenon_L312_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e0) = (e1))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e0))) -> (~((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 (e2) (e2)) = (e2)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hde zenon_H18a zenon_H38 zenon_Hdc zenon_H11f zenon_Hd9 zenon_H1ad zenon_H6d zenon_Hee zenon_H46 zenon_H13f zenon_H191 zenon_H1f zenon_H17d zenon_H52. % 5.66/5.82 apply (zenon_L311_); trivial. % 5.66/5.82 (* end of lemma zenon_L312_ *) % 5.66/5.82 assert (zenon_L313_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H36 zenon_H4a zenon_H11f zenon_H77 zenon_H4d. % 5.66/5.82 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.66/5.82 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_Hd6. zenon_intro zenon_H4c. % 5.66/5.82 apply (zenon_L98_); trivial. % 5.66/5.82 (* end of lemma zenon_L313_ *) % 5.66/5.82 assert (zenon_L314_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H17d zenon_H39 zenon_H122 zenon_H13f zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H14b zenon_H3d. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.82 apply (zenon_L112_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.82 exact (zenon_H13f zenon_H28). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.82 apply (zenon_L179_); trivial. % 5.66/5.82 apply (zenon_L180_); trivial. % 5.66/5.82 (* end of lemma zenon_L314_ *) % 5.66/5.82 assert (zenon_L315_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H3b zenon_H17d zenon_H122 zenon_H13f zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H14b. % 5.66/5.82 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.66/5.82 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.66/5.82 apply (zenon_L314_); trivial. % 5.66/5.82 (* end of lemma zenon_L315_ *) % 5.66/5.82 assert (zenon_L316_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hc5 zenon_H195 zenon_H194 zenon_H188 zenon_H17d zenon_H174 zenon_H171 zenon_H179 zenon_H16e zenon_H163 zenon_H169 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H8e zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H18a zenon_H32 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H53 zenon_H1f zenon_H55 zenon_H59 zenon_H58 zenon_H57 zenon_H63 zenon_Hf7 zenon_Hf8. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.82 apply (zenon_L264_); trivial. % 5.66/5.82 (* end of lemma zenon_L316_ *) % 5.66/5.82 assert (zenon_L317_ : ((op (e2) (e3)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hcd zenon_Ha4 zenon_H129. % 5.66/5.82 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H175 | zenon_intro zenon_H176 ]. % 5.66/5.82 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e2) (e1)) = (op (e2) (e3)))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H129. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H175. % 5.66/5.82 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 5.66/5.82 cut (((op (e2) (e3)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 5.66/5.82 congruence. % 5.66/5.82 cut (((op (e2) (e3)) = (e3)) = ((op (e2) (e3)) = (op (e2) (e1)))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1ae. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Hcd. % 5.66/5.82 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 5.66/5.82 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 5.66/5.82 congruence. % 5.66/5.82 apply zenon_H176. apply refl_equal. % 5.66/5.82 apply zenon_H1af. apply sym_equal. exact zenon_Ha4. % 5.66/5.82 apply zenon_H176. apply refl_equal. % 5.66/5.82 apply zenon_H176. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L317_ *) % 5.66/5.82 assert (zenon_L318_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e3)) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Haa zenon_H9d zenon_H42 zenon_H26 zenon_H129 zenon_Hcd zenon_Hd1 zenon_H1a0. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hab ]. % 5.66/5.82 apply (zenon_L102_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H2d | zenon_intro zenon_Hac ]. % 5.66/5.82 exact (zenon_H26 zenon_H2d). % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha6 ]. % 5.66/5.82 apply (zenon_L317_); trivial. % 5.66/5.82 apply (zenon_L303_); trivial. % 5.66/5.82 (* end of lemma zenon_L318_ *) % 5.66/5.82 assert (zenon_L319_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H10a zenon_Hb8 zenon_H6d zenon_H31 zenon_H86 zenon_Hbe zenon_Hf3 zenon_Hd3. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.82 exact (zenon_Hb8 zenon_Hba). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.82 apply (zenon_L19_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.82 apply (zenon_L78_); trivial. % 5.66/5.82 apply (zenon_L278_); trivial. % 5.66/5.82 (* end of lemma zenon_L319_ *) % 5.66/5.82 assert (zenon_L320_ : (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e0)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H63 zenon_Hbe zenon_Hd6. % 5.66/5.82 cut (((op (e2) (e0)) = (e2)) = ((e0) = (e2))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H63. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Hbe. % 5.66/5.82 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.82 cut (((op (e2) (e0)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H1b0 zenon_Hd6). % 5.66/5.82 apply zenon_H62. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L320_ *) % 5.66/5.82 assert (zenon_L321_ : ((op (e0) (e3)) = (e1)) -> ((op (e0) (e3)) = (e2)) -> (~((e1) = (e2))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H14a zenon_H167 zenon_H97. % 5.66/5.82 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.66/5.82 cut (((e2) = (e2)) = ((e1) = (e2))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H97. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H69. % 5.66/5.82 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.82 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 5.66/5.82 congruence. % 5.66/5.82 cut (((op (e0) (e3)) = (e1)) = ((e2) = (e1))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H98. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H14a. % 5.66/5.82 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.82 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H168 zenon_H167). % 5.66/5.82 apply zenon_H94. apply refl_equal. % 5.66/5.82 apply zenon_H62. apply refl_equal. % 5.66/5.82 apply zenon_H62. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L321_ *) % 5.66/5.82 assert (zenon_L322_ : ((op (e1) (e3)) = (e0)) -> ((op (e1) (e3)) = (e2)) -> (~((e0) = (e2))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H56 zenon_H96 zenon_H63. % 5.66/5.82 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.66/5.82 cut (((e2) = (e2)) = ((e0) = (e2))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H63. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H69. % 5.66/5.82 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.82 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 5.66/5.82 congruence. % 5.66/5.82 cut (((op (e1) (e3)) = (e0)) = ((e2) = (e0))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H6a. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H56. % 5.66/5.82 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.82 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H99 zenon_H96). % 5.66/5.82 apply zenon_H67. apply refl_equal. % 5.66/5.82 apply zenon_H62. apply refl_equal. % 5.66/5.82 apply zenon_H62. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L322_ *) % 5.66/5.82 assert (zenon_L323_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))) -> ((op (e3) (e3)) = (e2)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H1b1 zenon_H61. % 5.66/5.82 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 5.66/5.82 cut (((op (e3) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H59]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H59 zenon_H61). % 5.66/5.82 exact (zenon_H59 zenon_H61). % 5.66/5.82 (* end of lemma zenon_L323_ *) % 5.66/5.82 assert (zenon_L324_ : ((op (e0) (e3)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H14a zenon_H4f zenon_H61. % 5.66/5.82 apply (zenon_notand_s _ _ ax18); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H1b2 ]. % 5.66/5.82 apply zenon_H1b3. apply sym_equal. exact zenon_H61. % 5.66/5.82 apply (zenon_notand_s _ _ zenon_H1b2); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H1b4 ]. % 5.66/5.82 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1b5. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H1b6. % 5.66/5.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 5.66/5.82 congruence. % 5.66/5.82 cut (((op (e2) (e2)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1b8. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H4f. % 5.66/5.82 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.82 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b9]. % 5.66/5.82 congruence. % 5.66/5.82 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1b9. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H1b6. % 5.66/5.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 5.66/5.82 congruence. % 5.66/5.82 apply (zenon_L323_); trivial. % 5.66/5.82 apply zenon_H1b7. apply refl_equal. % 5.66/5.82 apply zenon_H1b7. apply refl_equal. % 5.66/5.82 apply zenon_H67. apply refl_equal. % 5.66/5.82 apply zenon_H1b7. apply refl_equal. % 5.66/5.82 apply zenon_H1b7. apply refl_equal. % 5.66/5.82 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.66/5.82 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1b4. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H1ba. % 5.66/5.82 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.66/5.82 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 5.66/5.82 congruence. % 5.66/5.82 cut (((op (e0) (e3)) = (e1)) = ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e1))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1bc. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H14a. % 5.66/5.82 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.82 cut (((op (e0) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bd]. % 5.66/5.82 congruence. % 5.66/5.82 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.66/5.82 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((op (e0) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1bd. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H1ba. % 5.66/5.82 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.66/5.82 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 5.66/5.82 congruence. % 5.66/5.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 5.66/5.82 congruence. % 5.66/5.82 cut (((op (e2) (e2)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1b8. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H4f. % 5.66/5.82 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.82 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b9]. % 5.66/5.82 congruence. % 5.66/5.82 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H1b9. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H1b6. % 5.66/5.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.82 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 5.66/5.82 congruence. % 5.66/5.82 apply (zenon_L323_); trivial. % 5.66/5.82 apply zenon_H1b7. apply refl_equal. % 5.66/5.82 apply zenon_H1b7. apply refl_equal. % 5.66/5.82 apply zenon_H67. apply refl_equal. % 5.66/5.82 apply zenon_H6f. apply refl_equal. % 5.66/5.82 apply zenon_H1bb. apply refl_equal. % 5.66/5.82 apply zenon_H1bb. apply refl_equal. % 5.66/5.82 apply zenon_H94. apply refl_equal. % 5.66/5.82 apply zenon_H1bb. apply refl_equal. % 5.66/5.82 apply zenon_H1bb. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L324_ *) % 5.66/5.82 assert (zenon_L325_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e2)) = (e0)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H1bf zenon_H97 zenon_H63 zenon_H56 zenon_H86 zenon_Hcd zenon_H14a zenon_H4f. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H167 | zenon_intro zenon_H1c0 ]. % 5.66/5.82 apply (zenon_L321_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H96 | zenon_intro zenon_H1c1 ]. % 5.66/5.82 apply (zenon_L322_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H64 | zenon_intro zenon_H61 ]. % 5.66/5.82 apply (zenon_L282_); trivial. % 5.66/5.82 apply (zenon_L324_); trivial. % 5.66/5.82 (* end of lemma zenon_L325_ *) % 5.66/5.82 assert (zenon_L326_ : (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (e3)) = (e0)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H6d zenon_Hcd zenon_H65. % 5.66/5.82 cut (((op (e2) (e3)) = (e3)) = ((e0) = (e3))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H6d. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Hcd. % 5.66/5.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.82 cut (((op (e2) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H66 zenon_H65). % 5.66/5.82 apply zenon_H6f. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L326_ *) % 5.66/5.82 assert (zenon_L327_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e3) (e2)) = (e3)) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e3)) = (e0)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H140 zenon_H13f zenon_Hf7 zenon_Hd3 zenon_H38 zenon_H1f zenon_H126 zenon_H1c2 zenon_H9d zenon_Ha1 zenon_H24 zenon_Hcd zenon_H6d zenon_H1bf zenon_H97 zenon_H63 zenon_H56 zenon_H86 zenon_H14a zenon_Hbe zenon_H18e zenon_Hee. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.66/5.82 apply (zenon_L40_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.66/5.82 exact (zenon_H13f zenon_H28). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H42 | zenon_intro zenon_H1c3 ]. % 5.66/5.82 apply (zenon_L102_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c4 ]. % 5.66/5.82 exact (zenon_H24 zenon_H2c). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Haf ]. % 5.66/5.82 apply (zenon_L122_); trivial. % 5.66/5.82 apply (zenon_L267_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H42 | zenon_intro zenon_H1c3 ]. % 5.66/5.82 apply (zenon_L102_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c4 ]. % 5.66/5.82 exact (zenon_H24 zenon_H2c). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Haf ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H18f ]. % 5.66/5.82 apply (zenon_L320_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H12f | zenon_intro zenon_H190 ]. % 5.66/5.82 apply (zenon_L122_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H4f | zenon_intro zenon_H65 ]. % 5.66/5.82 apply (zenon_L325_); trivial. % 5.66/5.82 apply (zenon_L326_); trivial. % 5.66/5.82 apply (zenon_L265_); trivial. % 5.66/5.82 (* end of lemma zenon_L327_ *) % 5.66/5.82 assert (zenon_L328_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e1) (e2)) = (e1)) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e3)) = (e0))) -> (~((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e1) (e1)) = (e1))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H14f zenon_H150 zenon_H1a0 zenon_Hd1 zenon_H129 zenon_Haa zenon_H1a6 zenon_H169 zenon_H16a zenon_H26 zenon_H23 zenon_H21 zenon_H9d zenon_H86 zenon_H17d zenon_Hf3 zenon_Hb8 zenon_H10a zenon_H46 zenon_H140 zenon_H13f zenon_Hf7 zenon_H38 zenon_H1f zenon_H126 zenon_H1c2 zenon_H24 zenon_H6d zenon_H1bf zenon_H63 zenon_Hbe zenon_H18e zenon_Hee zenon_Hb7 zenon_H97. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.82 exact (zenon_H150 zenon_H152). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.82 apply (zenon_L318_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.82 apply (zenon_L290_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.82 exact (zenon_H16a zenon_H16c). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.82 apply (zenon_L169_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.82 exact (zenon_Hb8 zenon_Hba). % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.82 apply (zenon_L319_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.82 exact (zenon_H13f zenon_H28). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.82 apply (zenon_L300_); trivial. % 5.66/5.82 apply (zenon_L327_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.82 apply (zenon_L45_); trivial. % 5.66/5.82 apply (zenon_L272_); trivial. % 5.66/5.82 apply (zenon_L321_); trivial. % 5.66/5.82 (* end of lemma zenon_L328_ *) % 5.66/5.82 assert (zenon_L329_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hc5 zenon_Hf0 zenon_Hbe. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.82 apply (zenon_L84_); trivial. % 5.66/5.82 (* end of lemma zenon_L329_ *) % 5.66/5.82 assert (zenon_L330_ : (~((e0) = (e2))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e0)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H63 zenon_Hc7 zenon_H78. % 5.66/5.82 cut (((op (e3) (e2)) = (e2)) = ((e0) = (e2))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H63. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Hc7. % 5.66/5.82 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.82 cut (((op (e3) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H197 zenon_H78). % 5.66/5.82 apply zenon_H62. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L330_ *) % 5.66/5.82 assert (zenon_L331_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (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 (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hc5 zenon_H126 zenon_H1f zenon_H38 zenon_Ha6 zenon_H6d zenon_H63 zenon_Hf7. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H39 | zenon_intro zenon_H127 ]. % 5.66/5.82 apply (zenon_L6_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H124 | zenon_intro zenon_H128 ]. % 5.66/5.82 apply (zenon_L287_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H78 | zenon_intro zenon_H5b ]. % 5.66/5.82 apply (zenon_L330_); trivial. % 5.66/5.82 exact (zenon_Hf7 zenon_H5b). % 5.66/5.82 (* end of lemma zenon_L331_ *) % 5.66/5.82 assert (zenon_L332_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> False). % 5.66/5.82 do 0 intro. intros zenon_Had zenon_H9a zenon_H41. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.66/5.82 apply (zenon_L33_); trivial. % 5.66/5.82 (* end of lemma zenon_L332_ *) % 5.66/5.82 assert (zenon_L333_ : ((op (e1) (e0)) = (e1)) -> ((op (e1) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H41 zenon_H68 zenon_H97. % 5.66/5.82 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.66/5.82 cut (((e2) = (e2)) = ((e1) = (e2))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H97. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H69. % 5.66/5.82 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.82 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 5.66/5.82 congruence. % 5.66/5.82 cut (((op (e1) (e0)) = (e1)) = ((e2) = (e1))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H98. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H41. % 5.66/5.82 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.82 cut (((op (e1) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H6b zenon_H68). % 5.66/5.82 apply zenon_H94. apply refl_equal. % 5.66/5.82 apply zenon_H62. apply refl_equal. % 5.66/5.82 apply zenon_H62. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L333_ *) % 5.66/5.82 assert (zenon_L334_ : (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e2)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H86 zenon_Hca zenon_H1c5. % 5.66/5.82 cut (((op (e3) (e0)) = (e3)) = ((e2) = (e3))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H86. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Hca. % 5.66/5.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.82 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H1c6 zenon_H1c5). % 5.66/5.82 apply zenon_H6f. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L334_ *) % 5.66/5.82 assert (zenon_L335_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H1c7 zenon_H16a zenon_H97 zenon_H41 zenon_H110 zenon_Hc0 zenon_H86 zenon_Hca. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.66/5.82 exact (zenon_H16a zenon_H16c). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.66/5.82 apply (zenon_L333_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.66/5.82 apply (zenon_L83_); trivial. % 5.66/5.82 apply (zenon_L334_); trivial. % 5.66/5.82 (* end of lemma zenon_L335_ *) % 5.66/5.82 assert (zenon_L336_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H1c7 zenon_H16a zenon_H97 zenon_H41 zenon_H64 zenon_Hf0 zenon_H86 zenon_Hca. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.66/5.82 exact (zenon_H16a zenon_H16c). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.66/5.82 apply (zenon_L333_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.66/5.82 apply (zenon_L84_); trivial. % 5.66/5.82 apply (zenon_L334_); trivial. % 5.66/5.82 (* end of lemma zenon_L336_ *) % 5.66/5.82 assert (zenon_L337_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hde zenon_H18a zenon_H32 zenon_H6d zenon_H9f zenon_H9a zenon_H110 zenon_H86 zenon_Hf0 zenon_H41 zenon_H97 zenon_H16a zenon_H1c7 zenon_H1f zenon_H143 zenon_Hca zenon_Hf3. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.82 apply (zenon_L1_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.82 apply (zenon_L238_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.82 apply (zenon_L5_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.82 apply (zenon_L305_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.82 apply (zenon_L8_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.82 apply (zenon_L9_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.82 apply (zenon_L106_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.82 apply (zenon_L332_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.82 apply (zenon_L242_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.82 apply (zenon_L335_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.82 apply (zenon_L51_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.82 apply (zenon_L336_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.82 apply (zenon_L243_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.82 apply (zenon_L307_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.82 apply (zenon_L308_); trivial. % 5.66/5.82 apply (zenon_L284_); trivial. % 5.66/5.82 (* end of lemma zenon_L337_ *) % 5.66/5.82 assert (zenon_L338_ : (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> ((op (e2) (e0)) = (e1)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H97 zenon_Hbe zenon_H12b. % 5.66/5.82 cut (((op (e2) (e0)) = (e2)) = ((e1) = (e2))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H97. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Hbe. % 5.66/5.82 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.82 cut (((op (e2) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H12e zenon_H12b). % 5.66/5.82 apply zenon_H62. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L338_ *) % 5.66/5.82 assert (zenon_L339_ : (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e3) (e0)) = (e1)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H9d zenon_Hca zenon_H182. % 5.66/5.82 cut (((op (e3) (e0)) = (e3)) = ((e1) = (e3))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H9d. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Hca. % 5.66/5.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.82 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H1ca zenon_H182). % 5.66/5.82 apply zenon_H6f. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L339_ *) % 5.66/5.82 assert (zenon_L340_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((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) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H1cb zenon_H150 zenon_Hf3 zenon_H143 zenon_H1f zenon_H1c7 zenon_H16a zenon_Hf0 zenon_H86 zenon_H110 zenon_H9a zenon_H9f zenon_H6d zenon_H32 zenon_H18a zenon_Hde zenon_Hbe zenon_H97 zenon_H9d zenon_Hca. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.66/5.82 exact (zenon_H150 zenon_H152). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.66/5.82 apply (zenon_L337_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.66/5.82 apply (zenon_L338_); trivial. % 5.66/5.82 apply (zenon_L339_); trivial. % 5.66/5.82 (* end of lemma zenon_L340_ *) % 5.66/5.82 assert (zenon_L341_ : ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H1f zenon_H18a zenon_H52 zenon_H38 zenon_H46 zenon_Hdc zenon_H11f zenon_Hd9 zenon_H1ad zenon_H191 zenon_H13f zenon_Hee zenon_H6d zenon_H17d zenon_Hde. % 5.66/5.82 apply (zenon_L312_); trivial. % 5.66/5.82 (* end of lemma zenon_L341_ *) % 5.66/5.82 assert (zenon_L342_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H1cb zenon_H1c7 zenon_H1c2 zenon_H1bf zenon_H150 zenon_H13f zenon_H26 zenon_H1a6 zenon_H195 zenon_H194 zenon_H188 zenon_H17d zenon_H174 zenon_H171 zenon_H179 zenon_H16e zenon_H163 zenon_H169 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H72 zenon_H86 zenon_H8e zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H18a zenon_H32 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H53 zenon_H1f zenon_H55 zenon_H57 zenon_H63 zenon_Hf8 zenon_H38 zenon_H24 zenon_H16a zenon_H198 zenon_Hb8 zenon_H1a0 zenon_H1a5 zenon_H45 zenon_H46 zenon_H4a zenon_H1ad. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.66/5.82 apply (zenon_L11_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.82 apply (zenon_L286_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.82 apply (zenon_L1_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.82 apply (zenon_L238_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.82 apply (zenon_L5_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.82 apply (zenon_L7_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.82 apply (zenon_L39_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.82 apply (zenon_L9_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.82 apply (zenon_L293_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.82 apply (zenon_L295_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.82 apply (zenon_L242_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.82 apply (zenon_L50_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.82 apply (zenon_L51_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.82 apply (zenon_L297_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.82 apply (zenon_L299_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.82 apply (zenon_L302_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.82 apply (zenon_L303_); trivial. % 5.66/5.82 apply (zenon_L284_); trivial. % 5.66/5.82 apply (zenon_L42_); trivial. % 5.66/5.82 apply (zenon_L280_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.82 apply (zenon_L1_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.82 apply (zenon_L238_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.82 apply (zenon_L5_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.82 apply (zenon_L305_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.82 apply (zenon_L8_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.82 apply (zenon_L9_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.82 apply (zenon_L241_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.82 apply (zenon_L306_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.82 apply (zenon_L173_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.82 apply (zenon_L138_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.82 apply (zenon_L51_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.82 apply (zenon_L297_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.82 apply (zenon_L243_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.82 apply (zenon_L307_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.82 apply (zenon_L308_); trivial. % 5.66/5.82 apply (zenon_L284_); trivial. % 5.66/5.82 apply (zenon_L312_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.82 apply (zenon_L1_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.82 apply (zenon_L238_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.82 apply (zenon_L313_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.82 apply (zenon_L315_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.82 apply (zenon_L39_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.82 apply (zenon_L9_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.82 apply (zenon_L293_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.82 apply (zenon_L306_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.82 apply (zenon_L242_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.82 apply (zenon_L50_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.82 apply (zenon_L51_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.82 apply (zenon_L316_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.82 apply (zenon_L243_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.82 apply (zenon_L302_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.82 apply (zenon_L328_); trivial. % 5.66/5.82 apply (zenon_L284_); trivial. % 5.66/5.82 apply (zenon_L262_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.82 apply (zenon_L1_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.82 apply (zenon_L238_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.82 apply (zenon_L5_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.82 apply (zenon_L7_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.82 apply (zenon_L8_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.82 apply (zenon_L9_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.82 exact (zenon_H150 zenon_H152). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.82 apply (zenon_L289_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.82 apply (zenon_L290_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.82 exact (zenon_Hb8 zenon_Hba). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.82 apply (zenon_L19_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.82 exact (zenon_H13f zenon_H28). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.82 apply (zenon_L179_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H33 | zenon_intro zenon_H92 ]. % 5.66/5.82 apply (zenon_L108_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H74 | zenon_intro zenon_H93 ]. % 5.66/5.82 apply (zenon_L179_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H4f | zenon_intro zenon_H78 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H108 | zenon_intro zenon_H10e ]. % 5.66/5.82 apply (zenon_L78_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H10f ]. % 5.66/5.82 apply (zenon_L41_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H51 | zenon_intro zenon_Hcd ]. % 5.66/5.82 exact (zenon_H4d zenon_H51). % 5.66/5.82 apply (zenon_L325_); trivial. % 5.66/5.82 apply (zenon_L266_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.82 apply (zenon_L78_); trivial. % 5.66/5.82 apply (zenon_L278_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.82 apply (zenon_L268_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.82 apply (zenon_L242_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.82 apply (zenon_L83_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.82 apply (zenon_L51_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.82 apply (zenon_L329_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.82 apply (zenon_L279_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.82 apply (zenon_L281_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.82 apply (zenon_L328_); trivial. % 5.66/5.82 apply (zenon_L284_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.82 apply (zenon_L1_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.82 apply (zenon_L238_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.82 apply (zenon_L313_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.82 apply (zenon_L315_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.82 apply (zenon_L39_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.82 apply (zenon_L9_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd8). zenon_intro zenon_Ha3. zenon_intro zenon_H4c. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.82 exact (zenon_H150 zenon_H152). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.82 apply (zenon_L288_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.82 apply (zenon_L290_); trivial. % 5.66/5.82 apply (zenon_L292_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.82 apply (zenon_L295_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.82 apply (zenon_L242_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.82 apply (zenon_L50_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.82 apply (zenon_L51_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.82 apply (zenon_L331_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.82 apply (zenon_L299_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.82 apply (zenon_L302_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.82 apply (zenon_L303_); trivial. % 5.66/5.82 apply (zenon_L284_); trivial. % 5.66/5.82 apply (zenon_L42_); trivial. % 5.66/5.82 apply (zenon_L280_); trivial. % 5.66/5.82 apply (zenon_L340_); trivial. % 5.66/5.82 apply (zenon_L84_); trivial. % 5.66/5.82 apply (zenon_L341_); trivial. % 5.66/5.82 apply (zenon_L82_); trivial. % 5.66/5.82 (* end of lemma zenon_L342_ *) % 5.66/5.82 assert (zenon_L343_ : (((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (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)))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hd7 zenon_H1cb zenon_H1c7 zenon_H1c2 zenon_H1bf zenon_H150 zenon_H13f zenon_H26 zenon_H1a6 zenon_H195 zenon_H194 zenon_H188 zenon_H17d zenon_H174 zenon_H171 zenon_H179 zenon_H16e zenon_H163 zenon_H169 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H72 zenon_H86 zenon_H8e zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H18a zenon_H32 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H53 zenon_H1f zenon_H55 zenon_H57 zenon_H63 zenon_Hf8 zenon_H38 zenon_H24 zenon_H16a zenon_H198 zenon_Hb8 zenon_H1a0 zenon_H1a5 zenon_H45 zenon_H4a zenon_H1ad. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd7). zenon_intro zenon_H46. zenon_intro zenon_Hd8. % 5.66/5.82 apply (zenon_L342_); trivial. % 5.66/5.82 (* end of lemma zenon_L343_ *) % 5.66/5.82 assert (zenon_L344_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Had zenon_H14f zenon_H150 zenon_H123 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H14b. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.82 exact (zenon_H150 zenon_H152). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.82 apply (zenon_L194_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.82 apply (zenon_L133_); trivial. % 5.66/5.82 apply (zenon_L134_); trivial. % 5.66/5.82 (* end of lemma zenon_L344_ *) % 5.66/5.82 assert (zenon_L345_ : ((op (e1) (e3)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((e1) = (e3))) -> False). % 5.66/5.82 do 0 intro. intros zenon_H95 zenon_H89 zenon_H9d. % 5.66/5.82 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.66/5.82 cut (((e3) = (e3)) = ((e1) = (e3))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H9d. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H6e. % 5.66/5.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.82 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 5.66/5.82 congruence. % 5.66/5.82 cut (((op (e1) (e3)) = (e1)) = ((e3) = (e1))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H9e. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_H95. % 5.66/5.82 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.82 cut (((op (e1) (e3)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H1ce]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H1ce zenon_H89). % 5.66/5.82 apply zenon_H94. apply refl_equal. % 5.66/5.82 apply zenon_H6f. apply refl_equal. % 5.66/5.82 apply zenon_H6f. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L345_ *) % 5.66/5.82 assert (zenon_L346_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e3))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hcb zenon_H95 zenon_H9d. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.66/5.82 apply (zenon_L345_); trivial. % 5.66/5.82 (* end of lemma zenon_L346_ *) % 5.66/5.82 assert (zenon_L347_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H8f zenon_H11f zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H4b zenon_H6d zenon_Hd3. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H33 | zenon_intro zenon_H92 ]. % 5.66/5.82 apply (zenon_L98_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H74 | zenon_intro zenon_H93 ]. % 5.66/5.82 apply (zenon_L179_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H4f | zenon_intro zenon_H78 ]. % 5.66/5.82 exact (zenon_H4b zenon_H4f). % 5.66/5.82 apply (zenon_L266_); trivial. % 5.66/5.82 (* end of lemma zenon_L347_ *) % 5.66/5.82 assert (zenon_L348_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> False). % 5.66/5.82 do 0 intro. intros zenon_Hd1 zenon_H8f zenon_H11f zenon_H4d zenon_H77 zenon_H45 zenon_H4a zenon_H4b zenon_H6d. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.66/5.82 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.66/5.82 apply (zenon_L347_); trivial. % 5.66/5.82 (* end of lemma zenon_L348_ *) % 5.66/5.82 assert (zenon_L349_ : (~((e0) = (e2))) -> ((op (e2) (e1)) = (e2)) -> ((op (e2) (e1)) = (e0)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H63 zenon_Hc2 zenon_H12f. % 5.66/5.82 cut (((op (e2) (e1)) = (e2)) = ((e0) = (e2))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H63. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Hc2. % 5.66/5.82 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.82 cut (((op (e2) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H130]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H130 zenon_H12f). % 5.66/5.82 apply zenon_H62. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L349_ *) % 5.66/5.82 assert (zenon_L350_ : (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e1)) = (e2)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H86 zenon_Ha6 zenon_H1cf. % 5.66/5.82 cut (((op (e3) (e1)) = (e3)) = ((e2) = (e3))). % 5.66/5.82 intro zenon_D_pnotp. % 5.66/5.82 apply zenon_H86. % 5.66/5.82 rewrite <- zenon_D_pnotp. % 5.66/5.82 exact zenon_Ha6. % 5.66/5.82 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.82 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 5.66/5.82 congruence. % 5.66/5.82 exact (zenon_H1d0 zenon_H1cf). % 5.66/5.82 apply zenon_H6f. apply refl_equal. % 5.66/5.82 (* end of lemma zenon_L350_ *) % 5.66/5.82 assert (zenon_L351_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H1d1 zenon_H97 zenon_H42 zenon_H25 zenon_H12f zenon_H63 zenon_H86 zenon_Ha6. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H15a | zenon_intro zenon_H1d2 ]. % 5.66/5.82 apply (zenon_L155_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H2e | zenon_intro zenon_H1d3 ]. % 5.66/5.82 exact (zenon_H25 zenon_H2e). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1cf ]. % 5.66/5.82 apply (zenon_L349_); trivial. % 5.66/5.82 apply (zenon_L350_); trivial. % 5.66/5.82 (* end of lemma zenon_L351_ *) % 5.66/5.82 assert (zenon_L352_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e0)) -> False). % 5.66/5.82 do 0 intro. intros zenon_H140 zenon_Hee zenon_H13f zenon_Ha6 zenon_H86 zenon_H63 zenon_H25 zenon_H42 zenon_H97 zenon_H1d1 zenon_H143 zenon_H39. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.66/5.82 apply (zenon_L154_); trivial. % 5.66/5.82 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.66/5.82 exact (zenon_H13f zenon_H28). % 5.66/5.82 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.66/5.82 apply (zenon_L351_); trivial. % 5.66/5.82 apply (zenon_L127_); trivial. % 5.66/5.82 (* end of lemma zenon_L352_ *) % 5.66/5.83 assert (zenon_L353_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H14f zenon_H150 zenon_H39 zenon_H143 zenon_H1d1 zenon_H97 zenon_H25 zenon_H63 zenon_H86 zenon_Ha6 zenon_H13f zenon_H140 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H3d zenon_Hee. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.83 exact (zenon_H150 zenon_H152). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.83 apply (zenon_L352_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.83 apply (zenon_L133_); trivial. % 5.66/5.83 apply (zenon_L161_); trivial. % 5.66/5.83 (* end of lemma zenon_L353_ *) % 5.66/5.83 assert (zenon_L354_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H3b zenon_H14f zenon_H150 zenon_H143 zenon_H1d1 zenon_H97 zenon_H25 zenon_H63 zenon_H86 zenon_Ha6 zenon_H13f zenon_H140 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_Hee. % 5.66/5.83 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.66/5.83 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.66/5.83 apply (zenon_L353_); trivial. % 5.66/5.83 (* end of lemma zenon_L354_ *) % 5.66/5.83 assert (zenon_L355_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (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 (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e1))) -> (~((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))))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((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 (e3) (e0)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 5.66/5.83 do 0 intro. intros zenon_Hde zenon_H18a zenon_H32 zenon_H4a zenon_H4b zenon_H11f zenon_H4c zenon_H4d zenon_H140 zenon_H86 zenon_H25 zenon_H97 zenon_H1d1 zenon_H150 zenon_H14f zenon_H9a zenon_Hdc zenon_Hee zenon_H13f zenon_H191 zenon_H17d zenon_Hf7 zenon_H63 zenon_H6d zenon_H38 zenon_H1f zenon_H126 zenon_H143 zenon_H9d zenon_H95 zenon_Ha6 zenon_H1a0. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.83 apply (zenon_L1_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.83 apply (zenon_L238_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.83 apply (zenon_L5_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.83 apply (zenon_L354_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.83 apply (zenon_L34_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.83 apply (zenon_L9_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.83 apply (zenon_L208_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.83 apply (zenon_L295_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.83 apply (zenon_L242_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.83 apply (zenon_L255_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.83 apply (zenon_L51_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.83 apply (zenon_L331_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.83 apply (zenon_L299_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.83 apply (zenon_L346_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.83 apply (zenon_L303_); trivial. % 5.66/5.83 apply (zenon_L284_); trivial. % 5.66/5.83 (* end of lemma zenon_L355_ *) % 5.66/5.83 assert (zenon_L356_ : ((op (e0) (e2)) = (e1)) -> ((op (e0) (e2)) = (e3)) -> (~((e1) = (e3))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H149 zenon_Hb1 zenon_H9d. % 5.66/5.83 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.66/5.83 cut (((e3) = (e3)) = ((e1) = (e3))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H9d. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H6e. % 5.66/5.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.83 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 5.66/5.83 congruence. % 5.66/5.83 cut (((op (e0) (e2)) = (e1)) = ((e3) = (e1))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H9e. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H149. % 5.66/5.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.83 cut (((op (e0) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 5.66/5.83 congruence. % 5.66/5.83 exact (zenon_Hb2 zenon_Hb1). % 5.66/5.83 apply zenon_H94. apply refl_equal. % 5.66/5.83 apply zenon_H6f. apply refl_equal. % 5.66/5.83 apply zenon_H6f. apply refl_equal. % 5.66/5.83 (* end of lemma zenon_L356_ *) % 5.66/5.83 assert (zenon_L357_ : ((op (e0) (e1)) = (e0)) -> ((op (e0) (e1)) = (e2)) -> (~((e0) = (e2))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H22 zenon_H15a zenon_H63. % 5.66/5.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.66/5.83 cut (((e2) = (e2)) = ((e0) = (e2))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H63. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H69. % 5.66/5.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.83 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 5.66/5.83 congruence. % 5.66/5.83 cut (((op (e0) (e1)) = (e0)) = ((e2) = (e0))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H6a. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H22. % 5.66/5.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.83 cut (((op (e0) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 5.66/5.83 congruence. % 5.66/5.83 exact (zenon_H15b zenon_H15a). % 5.66/5.83 apply zenon_H67. apply refl_equal. % 5.66/5.83 apply zenon_H62. apply refl_equal. % 5.66/5.83 apply zenon_H62. apply refl_equal. % 5.66/5.83 (* end of lemma zenon_L357_ *) % 5.66/5.83 assert (zenon_L358_ : (((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 (e3) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H169 zenon_H16a zenon_H63 zenon_H22 zenon_Hc7 zenon_H198 zenon_H64 zenon_H174. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.83 exact (zenon_H16a zenon_H16c). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.83 apply (zenon_L357_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.83 apply (zenon_L276_); trivial. % 5.66/5.83 apply (zenon_L170_); trivial. % 5.66/5.83 (* end of lemma zenon_L358_ *) % 5.66/5.83 assert (zenon_L359_ : ((op (e0) (e3)) = (e3)) -> ((op (e0) (e2)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> False). % 5.66/5.83 do 0 intro. intros zenon_Hb3 zenon_Hb1 zenon_H154. % 5.66/5.83 elim (classic ((op (e0) (e3)) = (op (e0) (e3)))); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H17c ]. % 5.66/5.83 cut (((op (e0) (e3)) = (op (e0) (e3))) = ((op (e0) (e2)) = (op (e0) (e3)))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H154. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H1d4. % 5.66/5.83 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 5.66/5.83 cut (((op (e0) (e3)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 5.66/5.83 congruence. % 5.66/5.83 cut (((op (e0) (e3)) = (e3)) = ((op (e0) (e3)) = (op (e0) (e2)))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H1d5. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_Hb3. % 5.66/5.83 cut (((e3) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 5.66/5.83 cut (((op (e0) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H17c]. % 5.66/5.83 congruence. % 5.66/5.83 apply zenon_H17c. apply refl_equal. % 5.66/5.83 apply zenon_H19c. apply sym_equal. exact zenon_Hb1. % 5.66/5.83 apply zenon_H17c. apply refl_equal. % 5.66/5.83 apply zenon_H17c. apply refl_equal. % 5.66/5.83 (* end of lemma zenon_L359_ *) % 5.66/5.83 assert (zenon_L360_ : ((op (e1) (e2)) = (e0)) -> ((op (e1) (e2)) = (e3)) -> (~((e0) = (e3))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H74 zenon_H85 zenon_H6d. % 5.66/5.83 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.66/5.83 cut (((e3) = (e3)) = ((e0) = (e3))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H6d. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H6e. % 5.66/5.83 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.83 cut (((e3) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 5.66/5.83 congruence. % 5.66/5.83 cut (((op (e1) (e2)) = (e0)) = ((e3) = (e0))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H70. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H74. % 5.66/5.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.83 cut (((op (e1) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 5.66/5.83 congruence. % 5.66/5.83 exact (zenon_H88 zenon_H85). % 5.66/5.83 apply zenon_H67. apply refl_equal. % 5.66/5.83 apply zenon_H6f. apply refl_equal. % 5.66/5.83 apply zenon_H6f. apply refl_equal. % 5.66/5.83 (* end of lemma zenon_L360_ *) % 5.66/5.83 assert (zenon_L361_ : (~((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))) -> ((op (e2) (e2)) = (e3)) -> False). % 5.66/5.83 do 0 intro. intros zenon_H1d6 zenon_H51. % 5.66/5.83 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 5.66/5.83 cut (((op (e2) (e2)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 5.66/5.83 congruence. % 5.66/5.83 exact (zenon_H4d zenon_H51). % 5.66/5.83 exact (zenon_H4d zenon_H51). % 5.66/5.83 (* end of lemma zenon_L361_ *) % 5.66/5.83 assert (zenon_L362_ : (((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)) = (e1)) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e2)) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e2) (e2)) = (e3)) -> False). % 5.66/5.83 do 0 intro. intros zenon_H126 zenon_H1f zenon_H38 zenon_Haf zenon_Hee zenon_Hc7 zenon_H63 zenon_H149 zenon_H51. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H39 | zenon_intro zenon_H127 ]. % 5.66/5.83 apply (zenon_L6_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H124 | zenon_intro zenon_H128 ]. % 5.66/5.83 apply (zenon_L265_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H78 | zenon_intro zenon_H5b ]. % 5.66/5.83 apply (zenon_L330_); trivial. % 5.66/5.83 apply (zenon_notand_s _ _ ax24); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H1d7 ]. % 5.66/5.83 apply zenon_H1d8. apply sym_equal. exact zenon_H51. % 5.66/5.83 apply (zenon_notand_s _ _ zenon_H1d7); [ zenon_intro zenon_H1d9 | zenon_intro zenon_H160 ]. % 5.66/5.83 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.66/5.83 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e0) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H1d9. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H7c. % 5.66/5.83 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.66/5.83 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 5.66/5.83 congruence. % 5.66/5.83 cut (((op (e3) (e3)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H1da. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H5b. % 5.66/5.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.83 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 5.66/5.83 congruence. % 5.66/5.83 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.66/5.83 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H1db. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H7c. % 5.66/5.83 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.66/5.83 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 5.66/5.83 congruence. % 5.66/5.83 apply (zenon_L361_); trivial. % 5.66/5.83 apply zenon_H7d. apply refl_equal. % 5.66/5.83 apply zenon_H7d. apply refl_equal. % 5.66/5.83 apply zenon_H67. apply refl_equal. % 5.66/5.83 apply zenon_H7d. apply refl_equal. % 5.66/5.83 apply zenon_H7d. apply refl_equal. % 5.66/5.83 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H80 | zenon_intro zenon_H81 ]. % 5.66/5.83 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2))) = ((e1) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H160. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H80. % 5.66/5.83 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 5.66/5.83 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 5.66/5.83 congruence. % 5.66/5.83 cut (((op (e0) (e2)) = (e1)) = ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (e1))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H162. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H149. % 5.66/5.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.83 cut (((op (e0) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 5.66/5.83 congruence. % 5.66/5.83 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H80 | zenon_intro zenon_H81 ]. % 5.66/5.83 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2))) = ((op (e0) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H1dc. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H80. % 5.66/5.83 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 5.66/5.83 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1dd]. % 5.66/5.83 congruence. % 5.66/5.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.83 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 5.66/5.83 congruence. % 5.66/5.83 cut (((op (e3) (e3)) = (e0)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e0))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H1da. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H5b. % 5.66/5.83 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.83 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 5.66/5.83 congruence. % 5.66/5.83 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.66/5.83 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H1db. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H7c. % 5.66/5.83 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.66/5.83 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 5.66/5.83 congruence. % 5.66/5.83 apply (zenon_L361_); trivial. % 5.66/5.83 apply zenon_H7d. apply refl_equal. % 5.66/5.83 apply zenon_H7d. apply refl_equal. % 5.66/5.83 apply zenon_H67. apply refl_equal. % 5.66/5.83 apply zenon_H62. apply refl_equal. % 5.66/5.83 apply zenon_H81. apply refl_equal. % 5.66/5.83 apply zenon_H81. apply refl_equal. % 5.66/5.83 apply zenon_H94. apply refl_equal. % 5.66/5.83 apply zenon_H81. apply refl_equal. % 5.66/5.83 apply zenon_H81. apply refl_equal. % 5.66/5.83 (* end of lemma zenon_L362_ *) % 5.66/5.83 assert (zenon_L363_ : (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> ((op (e3) (e2)) = (e1)) -> False). % 5.66/5.83 do 0 intro. intros zenon_H97 zenon_Hc7 zenon_H15e. % 5.66/5.83 cut (((op (e3) (e2)) = (e2)) = ((e1) = (e2))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H97. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_Hc7. % 5.66/5.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.83 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 5.66/5.83 congruence. % 5.66/5.83 exact (zenon_H1de zenon_H15e). % 5.66/5.83 apply zenon_H62. apply refl_equal. % 5.66/5.83 (* end of lemma zenon_L363_ *) % 5.66/5.83 assert (zenon_L364_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e0)) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H185 zenon_Hca zenon_H9d zenon_H124 zenon_Hee zenon_Hc7 zenon_H97 zenon_H58. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H182 | zenon_intro zenon_H186 ]. % 5.66/5.83 apply (zenon_L339_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Haf | zenon_intro zenon_H187 ]. % 5.66/5.83 apply (zenon_L265_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H15e | zenon_intro zenon_H5f ]. % 5.66/5.83 apply (zenon_L363_); trivial. % 5.66/5.83 exact (zenon_H58 zenon_H5f). % 5.66/5.83 (* end of lemma zenon_L364_ *) % 5.66/5.83 assert (zenon_L365_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e3) (e0)) = (op (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)))) -> (~((e0) = (e2))) -> ((op (e0) (e2)) = (e1)) -> ((op (e1) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e2)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H140 zenon_H174 zenon_H64 zenon_H198 zenon_H16a zenon_H169 zenon_H13f zenon_Hf3 zenon_H126 zenon_H1f zenon_H38 zenon_H63 zenon_H149 zenon_H74 zenon_H6d zenon_Hb3 zenon_H154 zenon_H1df zenon_H24 zenon_H15a zenon_H1c2 zenon_H185 zenon_Hca zenon_H9d zenon_Hee zenon_Hc7 zenon_H97 zenon_H58. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.66/5.83 apply (zenon_L358_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.66/5.83 exact (zenon_H13f zenon_H28). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H42 | zenon_intro zenon_H1c3 ]. % 5.66/5.83 apply (zenon_L155_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c4 ]. % 5.66/5.83 exact (zenon_H24 zenon_H2c). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Haf ]. % 5.66/5.83 apply (zenon_L122_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_Hb1 | zenon_intro zenon_H1e0 ]. % 5.66/5.83 apply (zenon_L359_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H85 | zenon_intro zenon_H1e1 ]. % 5.66/5.83 apply (zenon_L360_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1e1); [ zenon_intro zenon_H51 | zenon_intro zenon_Hd3 ]. % 5.66/5.83 apply (zenon_L362_); trivial. % 5.66/5.83 apply (zenon_L278_); trivial. % 5.66/5.83 apply (zenon_L364_); trivial. % 5.66/5.83 (* end of lemma zenon_L365_ *) % 5.66/5.83 assert (zenon_L366_ : ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H117 zenon_H113 zenon_H1cb zenon_Hb8 zenon_H17d zenon_Hee zenon_H45 zenon_H77 zenon_H4a zenon_H13f zenon_H6d zenon_H86 zenon_H9d zenon_H10a zenon_Hbe zenon_H97 zenon_H95 zenon_H9a zenon_H150 zenon_Hf0 zenon_H116. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.66/5.83 exact (zenon_H150 zenon_H152). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.66/5.83 apply (zenon_L33_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.66/5.83 apply (zenon_L338_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.83 exact (zenon_Hb8 zenon_Hba). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.83 apply (zenon_L19_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.83 exact (zenon_H13f zenon_H28). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.83 apply (zenon_L179_); trivial. % 5.66/5.83 apply (zenon_L67_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.83 apply (zenon_L78_); trivial. % 5.66/5.83 apply (zenon_L339_); trivial. % 5.66/5.83 apply (zenon_L84_); trivial. % 5.66/5.83 apply (zenon_L85_); trivial. % 5.66/5.83 (* end of lemma zenon_L366_ *) % 5.66/5.83 assert (zenon_L367_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e2)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (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)))) -> (~((e0) = (e2))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H14f zenon_H174 zenon_H64 zenon_H198 zenon_Hc7 zenon_H1c7 zenon_H58 zenon_H171 zenon_H140 zenon_H16a zenon_H169 zenon_Hf3 zenon_H126 zenon_H1f zenon_H38 zenon_H63 zenon_H154 zenon_H1df zenon_H24 zenon_H1c2 zenon_H185 zenon_Hb7 zenon_H116 zenon_Hf0 zenon_H150 zenon_H9a zenon_H97 zenon_H10a zenon_H9d zenon_H6d zenon_H13f zenon_H4a zenon_H77 zenon_H45 zenon_Hee zenon_H17d zenon_Hb8 zenon_H1cb zenon_H113 zenon_H117 zenon_H86 zenon_Hca zenon_H95 zenon_H14b. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.83 exact (zenon_H150 zenon_H152). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.83 exact (zenon_H16a zenon_H16c). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.83 apply (zenon_L155_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.83 apply (zenon_L276_); trivial. % 5.66/5.83 apply (zenon_L170_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.83 exact (zenon_H16a zenon_H16c). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.66/5.83 exact (zenon_H16a zenon_H16c). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.83 exact (zenon_Hb8 zenon_Hba). % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.83 apply (zenon_L269_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.83 apply (zenon_L356_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.83 apply (zenon_L18_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.83 exact (zenon_H13f zenon_H28). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.83 apply (zenon_L365_); trivial. % 5.66/5.83 apply (zenon_L273_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.66/5.83 apply (zenon_L366_); trivial. % 5.66/5.83 apply (zenon_L334_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.83 apply (zenon_L276_); trivial. % 5.66/5.83 apply (zenon_L170_); trivial. % 5.66/5.83 apply (zenon_L134_); trivial. % 5.66/5.83 (* end of lemma zenon_L367_ *) % 5.66/5.83 assert (zenon_L368_ : ((op (e3) (e1)) = (e1)) -> ((op (e3) (e1)) = (e2)) -> (~((e1) = (e2))) -> False). % 5.66/5.83 do 0 intro. intros zenon_Haf zenon_H1cf zenon_H97. % 5.66/5.83 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.66/5.83 cut (((e2) = (e2)) = ((e1) = (e2))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H97. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H69. % 5.66/5.83 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.83 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 5.66/5.83 congruence. % 5.66/5.83 cut (((op (e3) (e1)) = (e1)) = ((e2) = (e1))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H98. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_Haf. % 5.66/5.83 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.83 cut (((op (e3) (e1)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 5.66/5.83 congruence. % 5.66/5.83 exact (zenon_H1d0 zenon_H1cf). % 5.66/5.83 apply zenon_H94. apply refl_equal. % 5.66/5.83 apply zenon_H62. apply refl_equal. % 5.66/5.83 apply zenon_H62. apply refl_equal. % 5.66/5.83 (* end of lemma zenon_L368_ *) % 5.66/5.83 assert (zenon_L369_ : (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 5.66/5.83 do 0 intro. intros zenon_H1e2 zenon_H52 zenon_Hc7. % 5.66/5.83 cut (((op (e2) (e2)) = (e2)) = ((op (e2) (e2)) = (op (e3) (e2)))). % 5.66/5.83 intro zenon_D_pnotp. % 5.66/5.83 apply zenon_H1e2. % 5.66/5.83 rewrite <- zenon_D_pnotp. % 5.66/5.83 exact zenon_H52. % 5.66/5.83 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 5.66/5.83 cut (((op (e2) (e2)) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 5.66/5.83 congruence. % 5.66/5.83 apply zenon_H102. apply refl_equal. % 5.66/5.83 apply zenon_H19e. apply sym_equal. exact zenon_Hc7. % 5.66/5.83 (* end of lemma zenon_L369_ *) % 5.66/5.83 assert (zenon_L370_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H1e3 zenon_Hca zenon_H86 zenon_H97 zenon_Haf zenon_H52 zenon_H1e2 zenon_H59. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1e4 ]. % 5.66/5.83 apply (zenon_L334_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1e5 ]. % 5.66/5.83 apply (zenon_L368_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1e5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H61 ]. % 5.66/5.83 apply (zenon_L369_); trivial. % 5.66/5.83 exact (zenon_H59 zenon_H61). % 5.66/5.83 (* end of lemma zenon_L370_ *) % 5.66/5.83 assert (zenon_L371_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.83 do 0 intro. intros zenon_H1d1 zenon_H97 zenon_H42 zenon_H25 zenon_H52 zenon_Hd9 zenon_H86 zenon_Ha6. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H15a | zenon_intro zenon_H1d2 ]. % 5.66/5.83 apply (zenon_L155_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H2e | zenon_intro zenon_H1d3 ]. % 5.66/5.83 exact (zenon_H25 zenon_H2e). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1cf ]. % 5.66/5.83 apply (zenon_L60_); trivial. % 5.66/5.83 apply (zenon_L350_); trivial. % 5.66/5.83 (* end of lemma zenon_L371_ *) % 5.66/5.83 assert (zenon_L372_ : (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e2) (e1)) = (e0)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.83 do 0 intro. intros zenon_H1c2 zenon_H86 zenon_Hd9 zenon_H52 zenon_H25 zenon_H97 zenon_H1d1 zenon_H24 zenon_H12f zenon_Hee zenon_H9d zenon_Ha6. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H42 | zenon_intro zenon_H1c3 ]. % 5.66/5.83 apply (zenon_L371_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c4 ]. % 5.66/5.83 exact (zenon_H24 zenon_H2c). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Haf ]. % 5.66/5.83 apply (zenon_L122_); trivial. % 5.66/5.83 apply (zenon_L294_); trivial. % 5.66/5.83 (* end of lemma zenon_L372_ *) % 5.66/5.83 assert (zenon_L373_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (((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 (e3) (e3)) = (e0))) -> (((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 (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> (~((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))))) -> (~((e0) = (e1))) -> False). % 5.66/5.83 do 0 intro. intros zenon_Had zenon_H140 zenon_H18a zenon_H13f zenon_Hf7 zenon_H1e6 zenon_H59 zenon_H1e2 zenon_H1e3 zenon_H9d zenon_H24 zenon_H1d1 zenon_H97 zenon_H25 zenon_H52 zenon_Hd9 zenon_H86 zenon_H1c2 zenon_H6d zenon_H38 zenon_H1f zenon_H126 zenon_Hee. % 5.66/5.83 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.66/5.83 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.66/5.83 apply (zenon_L237_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.66/5.83 exact (zenon_H13f zenon_H28). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H39 | zenon_intro zenon_H127 ]. % 5.66/5.83 apply (zenon_L6_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H124 | zenon_intro zenon_H128 ]. % 5.66/5.83 apply (zenon_L265_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H78 | zenon_intro zenon_H5b ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_Hca | zenon_intro zenon_H1e7 ]. % 5.66/5.83 apply (zenon_L370_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H1e8 ]. % 5.66/5.83 apply (zenon_L372_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H60 ]. % 5.66/5.83 apply (zenon_L266_); trivial. % 5.66/5.83 exact (zenon_H3e zenon_H60). % 5.66/5.83 exact (zenon_Hf7 zenon_H5b). % 5.66/5.83 apply (zenon_L265_); trivial. % 5.66/5.83 (* end of lemma zenon_L373_ *) % 5.66/5.83 assert (zenon_L374_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.83 do 0 intro. intros zenon_H140 zenon_H1f zenon_H18a zenon_H13f zenon_H9d zenon_Hee zenon_H24 zenon_H1d1 zenon_H97 zenon_H25 zenon_H52 zenon_Hd9 zenon_H86 zenon_H1c2 zenon_H6d zenon_Ha6. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.66/5.83 apply (zenon_L237_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.66/5.83 exact (zenon_H13f zenon_H28). % 5.66/5.83 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.66/5.83 apply (zenon_L372_); trivial. % 5.66/5.83 apply (zenon_L287_); trivial. % 5.66/5.83 (* end of lemma zenon_L374_ *) % 5.66/5.83 assert (zenon_L375_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e3))) -> False). % 5.66/5.83 do 0 intro. intros zenon_Hcb zenon_H140 zenon_H1f zenon_H18a zenon_H13f zenon_H9d zenon_Hee zenon_H1d1 zenon_H97 zenon_H25 zenon_H52 zenon_Hd9 zenon_H86 zenon_H1c2 zenon_H6d. % 5.66/5.83 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.83 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.66/5.83 apply (zenon_L374_); trivial. % 5.66/5.83 (* end of lemma zenon_L375_ *) % 5.66/5.83 assert (zenon_L376_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (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))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.66/5.83 do 0 intro. intros zenon_Hde zenon_H18a zenon_Hf7 zenon_H6d zenon_H38 zenon_H126 zenon_H95 zenon_Hee zenon_H63 zenon_H13f zenon_H191 zenon_H17d zenon_H1ad zenon_H1f zenon_Hd3 zenon_H1a0 zenon_H52. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.83 apply (zenon_L1_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.83 apply (zenon_L238_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.83 apply (zenon_L58_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.83 apply (zenon_L7_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.83 apply (zenon_L8_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.83 apply (zenon_L9_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.83 apply (zenon_L59_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.83 apply (zenon_L268_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.83 apply (zenon_L242_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.83 apply (zenon_L255_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.83 apply (zenon_L62_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.83 apply (zenon_L310_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.83 apply (zenon_L243_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.83 apply (zenon_L281_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.83 apply (zenon_L63_); trivial. % 5.66/5.83 apply (zenon_L284_); trivial. % 5.66/5.83 (* end of lemma zenon_L376_ *) % 5.66/5.83 assert (zenon_L377_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 5.66/5.83 do 0 intro. intros zenon_Had zenon_H1e3 zenon_Hca zenon_H86 zenon_H97 zenon_H52 zenon_H1e2 zenon_H59. % 5.66/5.83 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.66/5.83 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.66/5.83 apply (zenon_L370_); trivial. % 5.66/5.83 (* end of lemma zenon_L377_ *) % 5.66/5.83 assert (zenon_L378_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (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)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H100 zenon_H143 zenon_Hf3 zenon_H17d zenon_H191 zenon_H1f zenon_H63 zenon_H25 zenon_H45 zenon_H52 zenon_H97 zenon_H95 zenon_H105 zenon_H32 zenon_H38 zenon_H9a zenon_H24 zenon_Hdc zenon_H18a zenon_H13f zenon_H126 zenon_H1e3 zenon_H1e2 zenon_H86 zenon_H1c2 zenon_H9d zenon_Hd9 zenon_H1d1 zenon_H6d zenon_H1e6 zenon_Hee zenon_H140 zenon_H11f zenon_H1ad zenon_Hde zenon_H1a0 zenon_H1a5. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.83 apply (zenon_L1_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.83 apply (zenon_L76_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.83 apply (zenon_L5_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.83 apply (zenon_L7_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.83 apply (zenon_L34_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.83 apply (zenon_L9_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.83 apply (zenon_L208_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.83 apply (zenon_L373_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.83 apply (zenon_L190_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.83 apply (zenon_L61_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.83 apply (zenon_L62_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.83 apply (zenon_L310_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.83 apply (zenon_L243_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.83 apply (zenon_L375_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.83 apply (zenon_L63_); trivial. % 5.66/5.83 apply (zenon_L284_); trivial. % 5.66/5.83 apply (zenon_L376_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.83 apply (zenon_L1_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.83 apply (zenon_L76_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.83 apply (zenon_L5_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.83 apply (zenon_L7_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.83 apply (zenon_L34_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.83 apply (zenon_L9_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.83 apply (zenon_L208_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.83 apply (zenon_L377_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.83 apply (zenon_L190_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.83 apply (zenon_L61_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.83 apply (zenon_L62_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.83 apply (zenon_L310_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.83 apply (zenon_L243_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.83 apply (zenon_L307_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.83 apply (zenon_L63_); trivial. % 5.66/5.83 apply (zenon_L284_); trivial. % 5.66/5.83 apply (zenon_L278_); trivial. % 5.66/5.83 (* end of lemma zenon_L378_ *) % 5.66/5.83 assert (zenon_L379_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> False). % 5.66/5.83 do 0 intro. intros zenon_Hc5 zenon_H129 zenon_Hc2. % 5.66/5.83 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.83 apply (zenon_L118_); trivial. % 5.66/5.83 (* end of lemma zenon_L379_ *) % 5.66/5.83 assert (zenon_L380_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (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) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> False). % 5.66/5.83 do 0 intro. intros zenon_Hd1 zenon_H18e zenon_H1f zenon_H18c zenon_Hc2 zenon_H63 zenon_H4b zenon_H6d. % 5.66/5.83 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.66/5.83 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H18f ]. % 5.66/5.83 apply (zenon_L239_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H12f | zenon_intro zenon_H190 ]. % 5.66/5.83 apply (zenon_L349_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H4f | zenon_intro zenon_H65 ]. % 5.66/5.83 exact (zenon_H4b zenon_H4f). % 5.66/5.83 apply (zenon_L326_); trivial. % 5.66/5.83 (* end of lemma zenon_L380_ *) % 5.66/5.83 assert (zenon_L381_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H12a zenon_H110 zenon_H116 zenon_Hf0 zenon_H150 zenon_H9a zenon_H95 zenon_H97 zenon_Hbe zenon_H10a zenon_H9d zenon_H86 zenon_H6d zenon_H13f zenon_H4a zenon_H45 zenon_Hee zenon_H17d zenon_Hb8 zenon_H1cb zenon_H113 zenon_H117. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.66/5.83 apply (zenon_L366_); trivial. % 5.66/5.83 apply (zenon_L82_); trivial. % 5.66/5.83 (* end of lemma zenon_L381_ *) % 5.66/5.83 assert (zenon_L382_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (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) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> False). % 5.66/5.83 do 0 intro. intros zenon_H1e3 zenon_H1e2 zenon_H1e6 zenon_H1ad zenon_H198 zenon_H16a zenon_H1df zenon_H1c2 zenon_Hb8 zenon_H1cb zenon_H1c7 zenon_H1a5 zenon_H195 zenon_H194 zenon_H188 zenon_H174 zenon_H171 zenon_H179 zenon_H16e zenon_H163 zenon_H169 zenon_H12a zenon_H129 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hf0 zenon_Hdd zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H72 zenon_H86 zenon_H8e zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H32 zenon_H18e zenon_H18c zenon_H193 zenon_H53 zenon_H55 zenon_H57 zenon_Hf8 zenon_Hee zenon_H63 zenon_H191 zenon_H14f zenon_H123 zenon_H150 zenon_Hdc zenon_H24 zenon_H9a zenon_H95 zenon_H17d zenon_H14b zenon_H45 zenon_H13f zenon_H122 zenon_H4a zenon_H11f zenon_H18a zenon_H1f zenon_H25 zenon_H1d1 zenon_H38 zenon_H1a0 zenon_H1e9. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.83 apply (zenon_L1_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.83 apply (zenon_L238_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.83 apply (zenon_L313_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.83 apply (zenon_L315_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.83 apply (zenon_L34_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.83 apply (zenon_L9_); trivial. % 5.66/5.83 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L208_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L344_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L242_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L255_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L316_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L243_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L346_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L348_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 apply (zenon_L347_); trivial. % 5.66/5.84 apply (zenon_L355_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L5_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L305_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L208_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L344_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L242_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L255_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.66/5.84 apply (zenon_L367_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L243_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L307_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L308_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 apply (zenon_L298_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.84 apply (zenon_L286_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L5_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L7_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L34_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L208_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L295_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L242_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L255_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L331_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L299_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L346_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L303_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L5_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L305_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L241_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.84 exact (zenon_H150 zenon_H152). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.84 apply (zenon_L194_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.84 exact (zenon_H16a zenon_H16c). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.84 exact (zenon_Hb8 zenon_Hba). % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.84 apply (zenon_L269_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.84 apply (zenon_L356_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.84 apply (zenon_L246_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.84 exact (zenon_H13f zenon_H28). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1ea ]. % 5.66/5.84 apply (zenon_L156_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_H73 | zenon_intro zenon_H1eb ]. % 5.66/5.84 apply (zenon_L21_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1eb); [ zenon_intro zenon_H52 | zenon_intro zenon_Hc7 ]. % 5.66/5.84 exact (zenon_H4c zenon_H52). % 5.66/5.84 apply (zenon_L365_); trivial. % 5.66/5.84 apply (zenon_L67_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.84 apply (zenon_L156_); trivial. % 5.66/5.84 apply (zenon_L170_); trivial. % 5.66/5.84 apply (zenon_L134_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L173_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L138_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.66/5.84 apply (zenon_L367_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L243_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L307_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L308_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 apply (zenon_L298_); trivial. % 5.66/5.84 apply (zenon_L378_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L5_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L7_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L34_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L208_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L344_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L242_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L255_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L379_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L243_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L346_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L380_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 apply (zenon_L118_); trivial. % 5.66/5.84 apply (zenon_L60_); trivial. % 5.66/5.84 apply (zenon_L381_); trivial. % 5.66/5.84 (* end of lemma zenon_L382_ *) % 5.66/5.84 assert (zenon_L383_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e1) (e1)) = (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) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Had zenon_H1e3 zenon_H1e2 zenon_H1e6 zenon_H1ad zenon_H198 zenon_H16a zenon_H1df zenon_H1c2 zenon_Hb8 zenon_H1cb zenon_H1c7 zenon_H1a5 zenon_H195 zenon_H194 zenon_H188 zenon_H174 zenon_H171 zenon_H179 zenon_H16e zenon_H163 zenon_H169 zenon_H12a zenon_H129 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hf0 zenon_Hdd zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H72 zenon_H86 zenon_H8e zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H32 zenon_H18e zenon_H18c zenon_H193 zenon_H53 zenon_H55 zenon_H57 zenon_Hf8 zenon_Hee zenon_H63 zenon_H191 zenon_H14f zenon_H123 zenon_H150 zenon_Hdc zenon_H24 zenon_H9a zenon_H17d zenon_H14b zenon_H45 zenon_H13f zenon_H122 zenon_H4a zenon_H11f zenon_H18a zenon_H1f zenon_H25 zenon_H1d1 zenon_H38 zenon_H1a0 zenon_H1e9. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.66/5.84 apply (zenon_L382_); trivial. % 5.66/5.84 (* end of lemma zenon_L383_ *) % 5.66/5.84 assert (zenon_L384_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e0)) -> False). % 5.66/5.84 do 0 intro. intros zenon_Haa zenon_H9d zenon_H42 zenon_H26 zenon_H86 zenon_Hc2 zenon_H6d zenon_H124. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hab ]. % 5.66/5.84 apply (zenon_L102_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H2d | zenon_intro zenon_Hac ]. % 5.66/5.84 exact (zenon_H26 zenon_H2d). % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha6 ]. % 5.66/5.84 apply (zenon_L114_); trivial. % 5.66/5.84 apply (zenon_L287_); trivial. % 5.66/5.84 (* end of lemma zenon_L384_ *) % 5.66/5.84 assert (zenon_L385_ : (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e3))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H140 zenon_Hee zenon_H13f zenon_H63 zenon_Haa zenon_H9d zenon_H42 zenon_H26 zenon_H86 zenon_Hc2 zenon_H6d. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.66/5.84 apply (zenon_L154_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.66/5.84 exact (zenon_H13f zenon_H28). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.66/5.84 apply (zenon_L349_); trivial. % 5.66/5.84 apply (zenon_L384_); trivial. % 5.66/5.84 (* end of lemma zenon_L385_ *) % 5.66/5.84 assert (zenon_L386_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e3) (e3)) = (e3))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H14f zenon_H150 zenon_H6d zenon_Hc2 zenon_H86 zenon_H26 zenon_H9d zenon_Haa zenon_H63 zenon_H13f zenon_Hee zenon_H140 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.84 exact (zenon_H150 zenon_H152). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.84 apply (zenon_L385_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.84 apply (zenon_L133_); trivial. % 5.66/5.84 apply (zenon_L292_); trivial. % 5.66/5.84 (* end of lemma zenon_L386_ *) % 5.66/5.84 assert (zenon_L387_ : (((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e3) (e3)) = (e3))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hc0 zenon_H14f zenon_H150 zenon_H6d zenon_H86 zenon_H26 zenon_H9d zenon_Haa zenon_H63 zenon_H13f zenon_Hee zenon_H140 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.66/5.84 apply (zenon_L386_); trivial. % 5.66/5.84 (* end of lemma zenon_L387_ *) % 5.66/5.84 assert (zenon_L388_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (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 (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hcb zenon_H17d zenon_H1f zenon_H191 zenon_H13f zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H6d. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.84 apply (zenon_L246_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.84 exact (zenon_H13f zenon_H28). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.84 apply (zenon_L179_); trivial. % 5.66/5.84 apply (zenon_L301_); trivial. % 5.66/5.84 (* end of lemma zenon_L388_ *) % 5.66/5.84 assert (zenon_L389_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e0) = (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))))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hde zenon_H18a zenon_H32 zenon_H4a zenon_H45 zenon_H116 zenon_H9a zenon_H86 zenon_H110 zenon_H41 zenon_H97 zenon_H16a zenon_H1c7 zenon_H129 zenon_Hca zenon_H143 zenon_H6d zenon_H4b zenon_H63 zenon_Hc2 zenon_H18c zenon_H1f zenon_H18e. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L5_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L305_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L143_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L332_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L117_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L335_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L379_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L243_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L307_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L380_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 (* end of lemma zenon_L389_ *) % 5.66/5.84 assert (zenon_L390_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (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)) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (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) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.84 do 0 intro. intros zenon_H1cb zenon_H150 zenon_H18e zenon_H1f zenon_H18c zenon_Hc2 zenon_H4b zenon_H6d zenon_H143 zenon_H129 zenon_H110 zenon_H9a zenon_H116 zenon_H45 zenon_H4a zenon_H32 zenon_H18a zenon_Hde zenon_H86 zenon_H97 zenon_H17d zenon_H13f zenon_H73 zenon_H63 zenon_H55 zenon_H57 zenon_H58 zenon_H59 zenon_H3e zenon_H16a zenon_H1c7 zenon_H9d zenon_Hca. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.66/5.84 exact (zenon_H150 zenon_H152). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.66/5.84 apply (zenon_L389_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.66/5.84 exact (zenon_H16a zenon_H16c). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.84 apply (zenon_L18_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.84 exact (zenon_H13f zenon_H28). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.84 apply (zenon_L21_); trivial. % 5.66/5.84 apply (zenon_L13_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.66/5.84 apply (zenon_L338_); trivial. % 5.66/5.84 apply (zenon_L334_); trivial. % 5.66/5.84 apply (zenon_L339_); trivial. % 5.66/5.84 (* end of lemma zenon_L390_ *) % 5.66/5.84 assert (zenon_L391_ : ((op (e3) (e1)) = (e3)) -> ((op (e0) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Ha6 zenon_Ha1 zenon_H123. % 5.66/5.84 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1ec | zenon_intro zenon_H1a1 ]. % 5.66/5.84 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e0) (e1)) = (op (e3) (e1)))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H123. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_H1ec. % 5.66/5.84 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 5.66/5.84 cut (((op (e3) (e1)) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 5.66/5.84 congruence. % 5.66/5.84 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e0) (e1)))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H1ed. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_Ha6. % 5.66/5.84 cut (((e3) = (op (e0) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 5.66/5.84 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 5.66/5.84 congruence. % 5.66/5.84 apply zenon_H1a1. apply refl_equal. % 5.66/5.84 apply zenon_H1ee. apply sym_equal. exact zenon_Ha1. % 5.66/5.84 apply zenon_H1a1. apply refl_equal. % 5.66/5.84 apply zenon_H1a1. apply refl_equal. % 5.66/5.84 (* end of lemma zenon_L391_ *) % 5.66/5.84 assert (zenon_L392_ : ((op (e1) (e3)) = (e3)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H89 zenon_Hb3 zenon_H14b. % 5.66/5.84 elim (classic ((op (e1) (e3)) = (op (e1) (e3)))); [ zenon_intro zenon_H14c | zenon_intro zenon_H5d ]. % 5.66/5.84 cut (((op (e1) (e3)) = (op (e1) (e3))) = ((op (e0) (e3)) = (op (e1) (e3)))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H14b. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_H14c. % 5.66/5.84 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 5.66/5.84 cut (((op (e1) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 5.66/5.84 congruence. % 5.66/5.84 cut (((op (e1) (e3)) = (e3)) = ((op (e1) (e3)) = (op (e0) (e3)))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H14d. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_H89. % 5.66/5.84 cut (((e3) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 5.66/5.84 cut (((op (e1) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 5.66/5.84 congruence. % 5.66/5.84 apply zenon_H5d. apply refl_equal. % 5.66/5.84 apply zenon_Hb6. apply sym_equal. exact zenon_Hb3. % 5.66/5.84 apply zenon_H5d. apply refl_equal. % 5.66/5.84 apply zenon_H5d. apply refl_equal. % 5.66/5.84 (* end of lemma zenon_L392_ *) % 5.66/5.84 assert (zenon_L393_ : (((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)) -> (~((e2) = (e3))) -> ((op (e0) (e2)) = (e2)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hb7 zenon_Hb8 zenon_H123 zenon_Ha6 zenon_H86 zenon_Hb0 zenon_H89 zenon_H14b. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.84 exact (zenon_Hb8 zenon_Hba). % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.84 apply (zenon_L391_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.84 apply (zenon_L45_); trivial. % 5.66/5.84 apply (zenon_L392_); trivial. % 5.66/5.84 (* end of lemma zenon_L393_ *) % 5.66/5.84 assert (zenon_L394_ : (((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 (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hb7 zenon_Hb8 zenon_H123 zenon_Ha6 zenon_H9d zenon_H149 zenon_H89 zenon_H14b. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.84 exact (zenon_Hb8 zenon_Hba). % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.84 apply (zenon_L391_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.84 apply (zenon_L356_); trivial. % 5.66/5.84 apply (zenon_L392_); trivial. % 5.66/5.84 (* end of lemma zenon_L394_ *) % 5.66/5.84 assert (zenon_L395_ : ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H100 zenon_H143 zenon_Hf3 zenon_H32 zenon_H1f zenon_H18a zenon_H52 zenon_H38 zenon_H24 zenon_H13f zenon_H126 zenon_H1e3 zenon_H1e2 zenon_H97 zenon_H86 zenon_H1c2 zenon_H9d zenon_H25 zenon_Hd9 zenon_H1d1 zenon_H6d zenon_H1e6 zenon_Hee zenon_H140 zenon_H1ad zenon_Hde zenon_H11f zenon_H1a0 zenon_H1a5. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L58_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L7_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L59_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L373_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L242_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L61_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L62_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L310_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L243_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L375_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L63_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L5_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L7_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L59_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L268_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L190_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L61_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L62_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L310_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L243_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L281_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L63_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L58_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L7_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L59_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L377_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L242_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L61_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L62_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L310_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L243_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L307_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L63_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 apply (zenon_L278_); trivial. % 5.66/5.84 (* end of lemma zenon_L395_ *) % 5.66/5.84 assert (zenon_L396_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e1))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H14f zenon_H150 zenon_H6d zenon_Hc2 zenon_H86 zenon_H26 zenon_H9d zenon_Haa zenon_H63 zenon_H13f zenon_H140 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H3d zenon_Hee. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.84 exact (zenon_H150 zenon_H152). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.84 apply (zenon_L385_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.84 apply (zenon_L133_); trivial. % 5.66/5.84 apply (zenon_L161_); trivial. % 5.66/5.84 (* end of lemma zenon_L396_ *) % 5.66/5.84 assert (zenon_L397_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H3b zenon_H14f zenon_H150 zenon_H6d zenon_Hc2 zenon_H86 zenon_H26 zenon_H9d zenon_Haa zenon_H63 zenon_H13f zenon_H140 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_Hee. % 5.66/5.84 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.66/5.84 apply (zenon_L396_); trivial. % 5.66/5.84 (* end of lemma zenon_L397_ *) % 5.66/5.84 assert (zenon_L398_ : (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e1) (e3)) = (e2)) -> False). % 5.66/5.84 do 0 intro. intros zenon_H86 zenon_H89 zenon_H96. % 5.66/5.84 cut (((op (e1) (e3)) = (e3)) = ((e2) = (e3))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H86. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_H89. % 5.66/5.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.84 cut (((op (e1) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 5.66/5.84 congruence. % 5.66/5.84 exact (zenon_H99 zenon_H96). % 5.66/5.84 apply zenon_H6f. apply refl_equal. % 5.66/5.84 (* end of lemma zenon_L398_ *) % 5.66/5.84 assert (zenon_L399_ : (((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)) = (e0)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 5.66/5.84 do 0 intro. intros zenon_H105 zenon_H97 zenon_H41 zenon_H25 zenon_H74 zenon_H63 zenon_H86 zenon_H89. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.66/5.84 apply (zenon_L333_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.66/5.84 exact (zenon_H25 zenon_H2e). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.66/5.84 apply (zenon_L21_); trivial. % 5.66/5.84 apply (zenon_L398_); trivial. % 5.66/5.84 (* end of lemma zenon_L399_ *) % 5.66/5.84 assert (zenon_L400_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 5.66/5.84 do 0 intro. intros zenon_H8e zenon_H9d zenon_H26 zenon_H73 zenon_H8f zenon_Hb0 zenon_H86 zenon_H63 zenon_H25 zenon_H41 zenon_H97 zenon_H105 zenon_H4b zenon_H6d zenon_Hd3. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.84 apply (zenon_L99_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.84 exact (zenon_H26 zenon_H2d). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.84 apply (zenon_L26_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H33 | zenon_intro zenon_H92 ]. % 5.66/5.84 apply (zenon_L176_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H74 | zenon_intro zenon_H93 ]. % 5.66/5.84 apply (zenon_L399_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H4f | zenon_intro zenon_H78 ]. % 5.66/5.84 exact (zenon_H4b zenon_H4f). % 5.66/5.84 apply (zenon_L266_); trivial. % 5.66/5.84 (* end of lemma zenon_L400_ *) % 5.66/5.84 assert (zenon_L401_ : (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> ((op (e0) (e3)) = (e2)) -> False). % 5.66/5.84 do 0 intro. intros zenon_H86 zenon_Hb3 zenon_H167. % 5.66/5.84 cut (((op (e0) (e3)) = (e3)) = ((e2) = (e3))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H86. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_Hb3. % 5.66/5.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.84 cut (((op (e0) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H168]. % 5.66/5.84 congruence. % 5.66/5.84 exact (zenon_H168 zenon_H167). % 5.66/5.84 apply zenon_H6f. apply refl_equal. % 5.66/5.84 (* end of lemma zenon_L401_ *) % 5.66/5.84 assert (zenon_L402_ : (((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)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hb7 zenon_Hb8 zenon_H9d zenon_H42 zenon_H198 zenon_Hd3 zenon_H86 zenon_H167. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.84 exact (zenon_Hb8 zenon_Hba). % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.84 apply (zenon_L102_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.84 apply (zenon_L270_); trivial. % 5.66/5.84 apply (zenon_L401_); trivial. % 5.66/5.84 (* end of lemma zenon_L402_ *) % 5.66/5.84 assert (zenon_L403_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e2)) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e1)) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hb7 zenon_Hb8 zenon_H86 zenon_H15a zenon_H198 zenon_Hd3 zenon_H9d zenon_H14a. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.84 exact (zenon_Hb8 zenon_Hba). % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.84 apply (zenon_L269_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.84 apply (zenon_L270_); trivial. % 5.66/5.84 apply (zenon_L272_); trivial. % 5.66/5.84 (* end of lemma zenon_L403_ *) % 5.66/5.84 assert (zenon_L404_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((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)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (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))))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hde zenon_H18a zenon_H32 zenon_H45 zenon_H116 zenon_Hf7 zenon_Hee zenon_H38 zenon_H126 zenon_H110 zenon_H97 zenon_H8e zenon_H9d zenon_H26 zenon_H8f zenon_H86 zenon_H25 zenon_H41 zenon_H105 zenon_Hb7 zenon_Hb8 zenon_H198 zenon_H16a zenon_H169 zenon_H4a zenon_H11f zenon_H4c zenon_H4d zenon_H150 zenon_H14f zenon_H129 zenon_Hf3 zenon_Hd3 zenon_H1a0 zenon_H6d zenon_H4b zenon_H63 zenon_Hc2 zenon_H18c zenon_H1f zenon_H18e. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L5_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L7_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L143_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L268_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L117_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.84 exact (zenon_H150 zenon_H152). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.84 exact (zenon_H16a zenon_H16c). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.84 apply (zenon_L155_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.84 apply (zenon_L400_); trivial. % 5.66/5.84 apply (zenon_L402_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.84 apply (zenon_L133_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.84 exact (zenon_H16a zenon_H16c). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.84 apply (zenon_L403_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.84 apply (zenon_L400_); trivial. % 5.66/5.84 apply (zenon_L321_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L379_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L279_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L281_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L380_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 (* end of lemma zenon_L404_ *) % 5.66/5.84 assert (zenon_L405_ : (((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))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e0)) -> False). % 5.66/5.84 do 0 intro. intros zenon_H8e zenon_H9d zenon_H41 zenon_H26 zenon_H86 zenon_H73 zenon_H6d zenon_H56. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.84 apply (zenon_L99_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.84 exact (zenon_H26 zenon_H2d). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.84 apply (zenon_L26_); trivial. % 5.66/5.84 apply (zenon_L301_); trivial. % 5.66/5.84 (* end of lemma zenon_L405_ *) % 5.66/5.84 assert (zenon_L406_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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 (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e1) (e3)) = (e1)) -> (~((e0) = (e1))) -> (~((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))))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((e0) = (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))))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hde zenon_H18a zenon_H32 zenon_H4a zenon_H45 zenon_H116 zenon_Hf7 zenon_H38 zenon_H126 zenon_H110 zenon_H95 zenon_Hee zenon_H13f zenon_H191 zenon_H17d zenon_H129 zenon_Hf3 zenon_Hd3 zenon_H1a0 zenon_H6d zenon_H4b zenon_H63 zenon_Hc2 zenon_H18c zenon_H1f zenon_H18e. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L5_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L7_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L143_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L268_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L117_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L255_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L379_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L279_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L281_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L380_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 (* end of lemma zenon_L406_ *) % 5.66/5.84 assert (zenon_L407_ : (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((op (e1) (e3)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H155 zenon_H56 zenon_H86 zenon_H26 zenon_H9d zenon_H8e zenon_H97 zenon_H73 zenon_H1f zenon_H18a zenon_H32 zenon_H38 zenon_H24 zenon_H4a zenon_H45 zenon_H4b zenon_H129 zenon_Hc2 zenon_H116 zenon_Hee zenon_H6d zenon_Hd3 zenon_Hf7 zenon_H126 zenon_H110 zenon_H191 zenon_H13f zenon_H63 zenon_H17d zenon_Hf3 zenon_H1a0 zenon_H18c zenon_H18e zenon_Hde. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H41 | zenon_intro zenon_H156 ]. % 5.66/5.84 apply (zenon_L405_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H2c | zenon_intro zenon_H157 ]. % 5.66/5.84 exact (zenon_H24 zenon_H2c). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H46 | zenon_intro zenon_H95 ]. % 5.66/5.84 apply (zenon_L49_); trivial. % 5.66/5.84 apply (zenon_L406_); trivial. % 5.66/5.84 (* end of lemma zenon_L407_ *) % 5.66/5.84 assert (zenon_L408_ : ((op (e1) (e0)) = (e2)) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e1))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H68 zenon_H155 zenon_H86 zenon_H26 zenon_H9d zenon_H8e zenon_H97 zenon_H73 zenon_H1f zenon_H18a zenon_H32 zenon_H38 zenon_H24 zenon_H4a zenon_H45 zenon_H4b zenon_H129 zenon_Hc2 zenon_H116 zenon_Hee zenon_H6d zenon_Hd3 zenon_Hf7 zenon_H126 zenon_H110 zenon_H191 zenon_H13f zenon_H63 zenon_H17d zenon_Hf3 zenon_H1a0 zenon_H18c zenon_H18e zenon_Hde. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.84 apply (zenon_L18_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.84 exact (zenon_H13f zenon_H28). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.84 apply (zenon_L21_); trivial. % 5.66/5.84 apply (zenon_L407_); trivial. % 5.66/5.84 (* end of lemma zenon_L408_ *) % 5.66/5.84 assert (zenon_L409_ : ((op (e2) (e0)) = (e1)) -> ((op (e2) (e0)) = (e3)) -> (~((e1) = (e3))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H12b zenon_H108 zenon_H9d. % 5.66/5.84 elim (classic ((e3) = (e3))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 5.66/5.84 cut (((e3) = (e3)) = ((e1) = (e3))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H9d. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_H6e. % 5.66/5.84 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.84 cut (((e3) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 5.66/5.84 congruence. % 5.66/5.84 cut (((op (e2) (e0)) = (e1)) = ((e3) = (e1))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H9e. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_H12b. % 5.66/5.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.84 cut (((op (e2) (e0)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 5.66/5.84 congruence. % 5.66/5.84 exact (zenon_H109 zenon_H108). % 5.66/5.84 apply zenon_H94. apply refl_equal. % 5.66/5.84 apply zenon_H6f. apply refl_equal. % 5.66/5.84 apply zenon_H6f. apply refl_equal. % 5.66/5.84 (* end of lemma zenon_L409_ *) % 5.66/5.84 assert (zenon_L410_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hde zenon_H26 zenon_H25 zenon_H23 zenon_H21 zenon_H4d zenon_H77 zenon_H11f zenon_H4a zenon_H6d zenon_H9f zenon_H41 zenon_H9a zenon_H110 zenon_Hbe zenon_Hf0 zenon_H1f zenon_H143 zenon_Hca zenon_Hf3. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L3_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L313_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L305_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L106_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L332_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L242_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L83_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L329_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L243_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L307_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L308_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 (* end of lemma zenon_L410_ *) % 5.66/5.84 assert (zenon_L411_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H10a zenon_Hb8 zenon_H9d zenon_H86 zenon_Hde zenon_H26 zenon_H25 zenon_H23 zenon_H21 zenon_H4d zenon_H77 zenon_H11f zenon_H4a zenon_H6d zenon_H9f zenon_H41 zenon_H9a zenon_H110 zenon_Hbe zenon_Hf0 zenon_H1f zenon_H143 zenon_Hf3. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.84 exact (zenon_Hb8 zenon_Hba). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.84 apply (zenon_L99_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.84 apply (zenon_L78_); trivial. % 5.66/5.84 apply (zenon_L410_); trivial. % 5.66/5.84 (* end of lemma zenon_L411_ *) % 5.66/5.84 assert (zenon_L412_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((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) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e3))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hcb zenon_H1cb zenon_H150 zenon_Hf3 zenon_H143 zenon_H1f zenon_Hf0 zenon_H110 zenon_H9a zenon_H9f zenon_H11f zenon_H21 zenon_H23 zenon_H25 zenon_H26 zenon_Hde zenon_H97 zenon_H10a zenon_Hb8 zenon_H6d zenon_H4a zenon_H45 zenon_H77 zenon_H4c zenon_H4d zenon_H13f zenon_H17d zenon_H86 zenon_Hbe zenon_H9d. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.66/5.84 exact (zenon_H150 zenon_H152). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.66/5.84 apply (zenon_L411_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.66/5.84 apply (zenon_L338_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.84 exact (zenon_Hb8 zenon_Hba). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.84 apply (zenon_L19_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.84 exact (zenon_H13f zenon_H28). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.84 apply (zenon_L179_); trivial. % 5.66/5.84 apply (zenon_L301_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.84 apply (zenon_L78_); trivial. % 5.66/5.84 apply (zenon_L339_); trivial. % 5.66/5.84 (* end of lemma zenon_L412_ *) % 5.66/5.84 assert (zenon_L413_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H10a zenon_Hb8 zenon_H9d zenon_H86 zenon_Hde zenon_H26 zenon_H25 zenon_H23 zenon_H21 zenon_H4d zenon_H77 zenon_H11f zenon_H4a zenon_H6d zenon_H9f zenon_H41 zenon_H9a zenon_H110 zenon_Hbe zenon_Hf0 zenon_H1f zenon_H143 zenon_Hf3. % 5.66/5.84 apply (zenon_L411_); trivial. % 5.66/5.84 (* end of lemma zenon_L413_ *) % 5.66/5.84 assert (zenon_L414_ : ((op (e3) (e2)) = (e3)) -> ((op (e1) (e2)) = (e3)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hd3 zenon_H85 zenon_H1ef. % 5.66/5.84 elim (classic ((op (e3) (e2)) = (op (e3) (e2)))); [ zenon_intro zenon_H199 | zenon_intro zenon_H19a ]. % 5.66/5.84 cut (((op (e3) (e2)) = (op (e3) (e2))) = ((op (e1) (e2)) = (op (e3) (e2)))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H1ef. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_H199. % 5.66/5.84 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 5.66/5.84 cut (((op (e3) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f0]. % 5.66/5.84 congruence. % 5.66/5.84 cut (((op (e3) (e2)) = (e3)) = ((op (e3) (e2)) = (op (e1) (e2)))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H1f0. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_Hd3. % 5.66/5.84 cut (((e3) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 5.66/5.84 cut (((op (e3) (e2)) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 5.66/5.84 congruence. % 5.66/5.84 apply zenon_H19a. apply refl_equal. % 5.66/5.84 apply zenon_H1f1. apply sym_equal. exact zenon_H85. % 5.66/5.84 apply zenon_H19a. apply refl_equal. % 5.66/5.84 apply zenon_H19a. apply refl_equal. % 5.66/5.84 (* end of lemma zenon_L414_ *) % 5.66/5.84 assert (zenon_L415_ : (((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 (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e0)) -> False). % 5.66/5.84 do 0 intro. intros zenon_H8e zenon_H9d zenon_H41 zenon_H26 zenon_H1ef zenon_Hd3 zenon_H6d zenon_H56. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.84 apply (zenon_L99_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.84 exact (zenon_H26 zenon_H2d). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.84 apply (zenon_L414_); trivial. % 5.66/5.84 apply (zenon_L301_); trivial. % 5.66/5.84 (* end of lemma zenon_L415_ *) % 5.66/5.84 assert (zenon_L416_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (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 (e1) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (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) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e1))) -> (((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)) = (op (e3) (e0)))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e2) (e0)) = (e2)) -> (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e1) = (e2))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H14f zenon_H1a0 zenon_H129 zenon_Haa zenon_H155 zenon_H1ef zenon_H8e zenon_H1a6 zenon_Hde zenon_H143 zenon_Hf0 zenon_H110 zenon_H9a zenon_H9f zenon_H11f zenon_H25 zenon_H150 zenon_H1cb zenon_H169 zenon_H16a zenon_H26 zenon_H23 zenon_H21 zenon_H9d zenon_H86 zenon_H10a zenon_Hb8 zenon_Hee zenon_H18e zenon_H63 zenon_H1bf zenon_H6d zenon_H24 zenon_H1c2 zenon_H126 zenon_H1f zenon_H38 zenon_Hf7 zenon_H13f zenon_H140 zenon_H4a zenon_H45 zenon_H77 zenon_H4d zenon_H17d zenon_Hbe zenon_Hd1 zenon_Hf3 zenon_Hb7 zenon_H97. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.84 exact (zenon_H150 zenon_H152). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.84 apply (zenon_L318_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.66/5.84 exact (zenon_H150 zenon_H152). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.66/5.84 apply (zenon_L413_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.66/5.84 apply (zenon_L338_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.84 exact (zenon_Hb8 zenon_Hba). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.84 apply (zenon_L19_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.84 exact (zenon_H13f zenon_H28). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.84 apply (zenon_L179_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_H41 | zenon_intro zenon_H156 ]. % 5.66/5.84 apply (zenon_L415_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H156); [ zenon_intro zenon_H2c | zenon_intro zenon_H157 ]. % 5.66/5.84 exact (zenon_H24 zenon_H2c). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_H46 | zenon_intro zenon_H95 ]. % 5.66/5.84 apply (zenon_L290_); trivial. % 5.66/5.84 apply (zenon_L67_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.84 apply (zenon_L78_); trivial. % 5.66/5.84 apply (zenon_L339_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.84 exact (zenon_H16a zenon_H16c). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.84 apply (zenon_L169_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.84 exact (zenon_Hb8 zenon_Hba). % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.84 exact (zenon_Hb8 zenon_Hba). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.84 apply (zenon_L19_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.84 exact (zenon_H13f zenon_H28). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.84 apply (zenon_L179_); trivial. % 5.66/5.84 apply (zenon_L327_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.84 apply (zenon_L78_); trivial. % 5.66/5.84 apply (zenon_L308_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.84 apply (zenon_L45_); trivial. % 5.66/5.84 apply (zenon_L272_); trivial. % 5.66/5.84 apply (zenon_L321_); trivial. % 5.66/5.84 (* end of lemma zenon_L416_ *) % 5.66/5.84 assert (zenon_L417_ : ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e2)) = (e3))\/(((op (e1) (e2)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e3) (e2)) = (e3))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((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)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H1f zenon_H18a zenon_H11f zenon_H4a zenon_H122 zenon_H13f zenon_H45 zenon_H14b zenon_H17d zenon_H24 zenon_H1ad zenon_H1a5 zenon_H1a0 zenon_Hb8 zenon_H198 zenon_H16a zenon_H38 zenon_Hf8 zenon_H63 zenon_H57 zenon_H55 zenon_H53 zenon_H193 zenon_H191 zenon_H18c zenon_H18e zenon_H32 zenon_H189 zenon_H185 zenon_H11e zenon_H11a zenon_H118 zenon_H100 zenon_Hfd zenon_H8e zenon_H86 zenon_H72 zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H129 zenon_H12a zenon_H169 zenon_H163 zenon_H16e zenon_H179 zenon_H171 zenon_H174 zenon_H188 zenon_H194 zenon_H195 zenon_H1a6 zenon_H26 zenon_H150 zenon_H1bf zenon_H1c2 zenon_H1c7 zenon_H1cb zenon_H1e9 zenon_H1d1 zenon_H25 zenon_H1df zenon_H1e6 zenon_H1e2 zenon_H1e3 zenon_Hbe zenon_H1ef. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L313_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L315_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L9_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L343_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L383_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L242_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L83_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L329_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L243_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L412_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L416_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 apply (zenon_L340_); trivial. % 5.66/5.84 apply (zenon_L84_); trivial. % 5.66/5.84 apply (zenon_L395_); trivial. % 5.66/5.84 apply (zenon_L82_); trivial. % 5.66/5.84 (* end of lemma zenon_L417_ *) % 5.66/5.84 assert (zenon_L418_ : ((op (e3) (e0)) = (e1)) -> ((op (e3) (e0)) = (e2)) -> (~((e1) = (e2))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H182 zenon_H1c5 zenon_H97. % 5.66/5.84 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.66/5.84 cut (((e2) = (e2)) = ((e1) = (e2))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H97. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_H69. % 5.66/5.84 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.84 cut (((e2) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 5.66/5.84 congruence. % 5.66/5.84 cut (((op (e3) (e0)) = (e1)) = ((e2) = (e1))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H98. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_H182. % 5.66/5.84 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.84 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 5.66/5.84 congruence. % 5.66/5.84 exact (zenon_H1c6 zenon_H1c5). % 5.66/5.84 apply zenon_H94. apply refl_equal. % 5.66/5.84 apply zenon_H62. apply refl_equal. % 5.66/5.84 apply zenon_H62. apply refl_equal. % 5.66/5.84 (* end of lemma zenon_L418_ *) % 5.66/5.84 assert (zenon_L419_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 5.66/5.84 do 0 intro. intros zenon_H14f zenon_H150 zenon_H6d zenon_Hc2 zenon_H86 zenon_H26 zenon_Haa zenon_H63 zenon_H13f zenon_Hee zenon_H140 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H9d zenon_Hb3. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.84 exact (zenon_H150 zenon_H152). % 5.66/5.84 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.84 apply (zenon_L385_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.84 apply (zenon_L133_); trivial. % 5.66/5.84 apply (zenon_L272_); trivial. % 5.66/5.84 (* end of lemma zenon_L419_ *) % 5.66/5.84 assert (zenon_L420_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hc8 zenon_H14f zenon_H150 zenon_H6d zenon_Hc2 zenon_H86 zenon_H26 zenon_Haa zenon_H63 zenon_H13f zenon_Hee zenon_H140 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H9d. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.66/5.84 apply (zenon_L419_); trivial. % 5.66/5.84 (* end of lemma zenon_L420_ *) % 5.66/5.84 assert (zenon_L421_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e1) (e1)) = (e1)) -> False). % 5.66/5.84 do 0 intro. intros zenon_Had zenon_H188 zenon_H2c. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.66/5.84 apply (zenon_L217_); trivial. % 5.66/5.84 (* end of lemma zenon_L421_ *) % 5.66/5.84 assert (zenon_L422_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e2) (e3)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H1a5 zenon_H1a0 zenon_Hb8 zenon_H198 zenon_H16a zenon_H4b zenon_H38 zenon_H77 zenon_H2c zenon_Hf8 zenon_Hf7 zenon_H64 zenon_H63 zenon_H57 zenon_H58 zenon_H55 zenon_H1f zenon_H53 zenon_H193 zenon_H191 zenon_H18c zenon_H18e zenon_H32 zenon_H18a zenon_H189 zenon_H185 zenon_H11e zenon_H11a zenon_H118 zenon_H45 zenon_H100 zenon_Hfd zenon_H8e zenon_H86 zenon_H72 zenon_H4a zenon_H8f zenon_H6d zenon_H97 zenon_H105 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hde zenon_Hdc zenon_Hdd zenon_Hf0 zenon_Hee zenon_Hed zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H169 zenon_H163 zenon_H16e zenon_H179 zenon_H171 zenon_H174 zenon_H17d zenon_H188 zenon_H194 zenon_H195. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.84 apply (zenon_L264_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L147_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L7_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L90_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L241_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L268_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L173_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L138_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L277_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L279_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L281_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L283_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 (* end of lemma zenon_L422_ *) % 5.66/5.84 assert (zenon_L423_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> (~((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 (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hde zenon_H32 zenon_H118 zenon_H11a zenon_H9d zenon_Hf7 zenon_H63 zenon_H6d zenon_H38 zenon_H1f zenon_H126 zenon_H143 zenon_H2c zenon_Ha6 zenon_H1a0. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L87_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L5_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L7_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L89_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L90_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L92_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L295_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L242_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L93_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L331_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.84 apply (zenon_L299_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.84 apply (zenon_L94_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.84 apply (zenon_L303_); trivial. % 5.66/5.84 apply (zenon_L284_); trivial. % 5.66/5.84 (* end of lemma zenon_L423_ *) % 5.66/5.84 assert (zenon_L424_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e1)) -> False). % 5.66/5.84 do 0 intro. intros zenon_H1f2 zenon_H2c zenon_Haf. % 5.66/5.84 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e3) (e1)))). % 5.66/5.84 intro zenon_D_pnotp. % 5.66/5.84 apply zenon_H1f2. % 5.66/5.84 rewrite <- zenon_D_pnotp. % 5.66/5.84 exact zenon_H2c. % 5.66/5.84 cut (((e1) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 5.66/5.84 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 5.66/5.84 congruence. % 5.66/5.84 apply zenon_H11c. apply refl_equal. % 5.66/5.84 apply zenon_H184. apply sym_equal. exact zenon_Haf. % 5.66/5.84 (* end of lemma zenon_L424_ *) % 5.66/5.84 assert (zenon_L425_ : (((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 (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.84 do 0 intro. intros zenon_H185 zenon_Hca zenon_H9d zenon_H2c zenon_H1f2 zenon_Hc7 zenon_H97 zenon_H58. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H182 | zenon_intro zenon_H186 ]. % 5.66/5.84 apply (zenon_L339_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Haf | zenon_intro zenon_H187 ]. % 5.66/5.84 apply (zenon_L424_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H15e | zenon_intro zenon_H5f ]. % 5.66/5.84 apply (zenon_L363_); trivial. % 5.66/5.84 exact (zenon_H58 zenon_H5f). % 5.66/5.84 (* end of lemma zenon_L425_ *) % 5.66/5.84 assert (zenon_L426_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> (((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)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.84 do 0 intro. intros zenon_Hc5 zenon_H185 zenon_Hca zenon_H9d zenon_H2c zenon_H1f2 zenon_H97 zenon_H58. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.84 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.66/5.84 apply (zenon_L425_); trivial. % 5.66/5.84 (* end of lemma zenon_L426_ *) % 5.66/5.84 assert (zenon_L427_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((e0) = (e3))) -> ((op (e3) (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) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> False). % 5.66/5.84 do 0 intro. intros zenon_H179 zenon_Hde zenon_Hf3 zenon_H143 zenon_H185 zenon_H1f2 zenon_H9d zenon_H129 zenon_Hf0 zenon_H188 zenon_H18e zenon_H63 zenon_H4b zenon_H18c zenon_H6d zenon_Hca zenon_H146 zenon_H64 zenon_H97 zenon_H77 zenon_H2c zenon_H11a zenon_Hee zenon_H18a zenon_H1f. % 5.66/5.84 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.84 apply (zenon_L1_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.84 apply (zenon_L238_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.84 apply (zenon_L147_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.84 apply (zenon_L305_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.84 apply (zenon_L8_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.84 apply (zenon_L90_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.84 apply (zenon_L241_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.84 apply (zenon_L421_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.84 apply (zenon_L173_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.84 apply (zenon_L138_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.84 apply (zenon_L51_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.84 apply (zenon_L426_); trivial. % 5.66/5.84 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.85 apply (zenon_L243_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.85 apply (zenon_L307_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.85 apply (zenon_L308_); trivial. % 5.66/5.85 apply (zenon_L284_); trivial. % 5.66/5.85 apply (zenon_L298_); trivial. % 5.66/5.85 (* end of lemma zenon_L427_ *) % 5.66/5.85 assert (zenon_L428_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.66/5.85 do 0 intro. intros zenon_Hde zenon_H18a zenon_H38 zenon_H188 zenon_H11f zenon_Hd9 zenon_H1ad zenon_H1f zenon_H2c zenon_H52. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.85 apply (zenon_L1_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.85 apply (zenon_L238_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.85 apply (zenon_L58_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.85 apply (zenon_L7_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.85 apply (zenon_L8_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.85 apply (zenon_L90_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.85 apply (zenon_L59_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.85 apply (zenon_L421_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.85 apply (zenon_L190_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.85 apply (zenon_L61_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.85 apply (zenon_L62_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.85 apply (zenon_L310_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.85 apply (zenon_L243_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.85 apply (zenon_L94_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.85 apply (zenon_L63_); trivial. % 5.66/5.85 apply (zenon_L284_); trivial. % 5.66/5.85 (* end of lemma zenon_L428_ *) % 5.66/5.85 assert (zenon_L429_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (((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)) = (op (e0) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 5.66/5.85 do 0 intro. intros zenon_H188 zenon_H11e zenon_Hdc zenon_H1a5 zenon_H1a0 zenon_H11f zenon_Hde zenon_H1ad zenon_H140 zenon_Hee zenon_H1e6 zenon_H6d zenon_H1d1 zenon_Hd9 zenon_H9d zenon_H1c2 zenon_H86 zenon_H97 zenon_H1e2 zenon_H1e3 zenon_H126 zenon_H13f zenon_H38 zenon_H52 zenon_H18a zenon_H1f zenon_H17d zenon_H191 zenon_H32 zenon_Hf3 zenon_H143 zenon_H100 zenon_H114. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.66/5.85 apply (zenon_L395_); trivial. % 5.66/5.85 apply (zenon_L341_); trivial. % 5.66/5.85 apply (zenon_L428_); trivial. % 5.66/5.85 (* end of lemma zenon_L429_ *) % 5.66/5.85 assert (zenon_L430_ : (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e2) (e3)) = (e1)) -> False). % 5.66/5.85 do 0 intro. intros zenon_H9d zenon_Hcd zenon_H144. % 5.66/5.85 cut (((op (e2) (e3)) = (e3)) = ((e1) = (e3))). % 5.66/5.85 intro zenon_D_pnotp. % 5.66/5.85 apply zenon_H9d. % 5.66/5.85 rewrite <- zenon_D_pnotp. % 5.66/5.85 exact zenon_Hcd. % 5.66/5.85 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.85 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 5.66/5.85 congruence. % 5.66/5.85 exact (zenon_H145 zenon_H144). % 5.66/5.85 apply zenon_H6f. apply refl_equal. % 5.66/5.85 (* end of lemma zenon_L430_ *) % 5.66/5.85 assert (zenon_L431_ : (((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))) -> (~((e1) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 5.66/5.85 do 0 intro. intros zenon_H146 zenon_Hbe zenon_H97 zenon_H2c zenon_H11a zenon_H77 zenon_H9d zenon_Hcd. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H12b | zenon_intro zenon_H147 ]. % 5.66/5.85 apply (zenon_L338_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H148 ]. % 5.66/5.85 apply (zenon_L91_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H47 | zenon_intro zenon_H144 ]. % 5.66/5.85 exact (zenon_H77 zenon_H47). % 5.66/5.85 apply (zenon_L430_); trivial. % 5.66/5.85 (* end of lemma zenon_L431_ *) % 5.66/5.85 assert (zenon_L432_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2))))) -> (((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))) -> (~((e1) = (e3))) -> False). % 5.66/5.85 do 0 intro. intros zenon_Hd1 zenon_H146 zenon_Hbe zenon_H97 zenon_H2c zenon_H11a zenon_H77 zenon_H9d. % 5.66/5.85 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.66/5.85 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.66/5.85 apply (zenon_L431_); trivial. % 5.66/5.85 (* end of lemma zenon_L432_ *) % 5.66/5.85 assert (zenon_L433_ : ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e0) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> False). % 5.66/5.85 do 0 intro. intros zenon_H12a zenon_H110 zenon_H1f zenon_H2c zenon_H32 zenon_H38 zenon_H118 zenon_H11a zenon_H188 zenon_Hbe zenon_Hf0 zenon_H97 zenon_H9d zenon_H146 zenon_Hde. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.85 apply (zenon_L1_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.85 apply (zenon_L87_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.85 apply (zenon_L5_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.85 apply (zenon_L7_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.85 apply (zenon_L89_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.85 apply (zenon_L90_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.85 apply (zenon_L92_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.85 apply (zenon_L421_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.85 apply (zenon_L242_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.85 apply (zenon_L93_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.85 apply (zenon_L51_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.85 apply (zenon_L329_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.85 apply (zenon_L243_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.85 apply (zenon_L94_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.85 apply (zenon_L432_); trivial. % 5.66/5.85 apply (zenon_L284_); trivial. % 5.66/5.85 apply (zenon_L82_); trivial. % 5.66/5.85 (* end of lemma zenon_L433_ *) % 5.66/5.85 assert (zenon_L434_ : (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((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) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (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) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 5.66/5.85 do 0 intro. intros zenon_H1f2 zenon_H1f zenon_H18a zenon_H32 zenon_H38 zenon_H2c zenon_H11a zenon_H188 zenon_H195 zenon_H194 zenon_H17d zenon_H174 zenon_H171 zenon_H179 zenon_H16e zenon_H163 zenon_H169 zenon_H11f zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hed zenon_Hee zenon_Hf0 zenon_Hdd zenon_Hdc zenon_Hde zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_Hd9 zenon_H117 zenon_H9a zenon_H105 zenon_H97 zenon_H6d zenon_H8f zenon_H4a zenon_H72 zenon_H86 zenon_H8e zenon_Hfd zenon_H100 zenon_H45 zenon_H118 zenon_H11e zenon_H185 zenon_H189 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H53 zenon_H55 zenon_H57 zenon_H63 zenon_Hf8 zenon_H16a zenon_H198 zenon_Hb8 zenon_H1a0 zenon_H1a5. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.85 apply (zenon_L1_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.85 apply (zenon_L238_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.85 apply (zenon_L5_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.85 apply (zenon_L7_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.85 apply (zenon_L8_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.85 apply (zenon_L90_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.85 apply (zenon_L92_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.85 apply (zenon_L421_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.85 apply (zenon_L242_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.85 apply (zenon_L93_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.85 apply (zenon_L51_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.85 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.85 apply (zenon_L422_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.85 apply (zenon_L243_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.85 apply (zenon_L94_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.85 apply (zenon_L348_); trivial. % 5.66/5.85 apply (zenon_L284_); trivial. % 5.66/5.85 apply (zenon_L423_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.85 apply (zenon_L1_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.85 apply (zenon_L87_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.85 apply (zenon_L5_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.85 apply (zenon_L305_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.85 apply (zenon_L89_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.85 apply (zenon_L90_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.85 apply (zenon_L92_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.85 apply (zenon_L421_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.85 apply (zenon_L242_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.85 apply (zenon_L93_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.85 apply (zenon_L51_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.85 apply (zenon_L426_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.85 apply (zenon_L243_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.85 apply (zenon_L307_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.85 apply (zenon_L308_); trivial. % 5.66/5.85 apply (zenon_L284_); trivial. % 5.66/5.85 apply (zenon_L298_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.85 apply (zenon_L422_); trivial. % 5.66/5.85 apply (zenon_L423_); trivial. % 5.66/5.85 apply (zenon_L427_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.85 apply (zenon_L1_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.85 apply (zenon_L87_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.85 apply (zenon_L5_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.85 apply (zenon_L7_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.85 apply (zenon_L89_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.85 apply (zenon_L90_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.85 apply (zenon_L92_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.85 apply (zenon_L421_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.85 apply (zenon_L242_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.85 apply (zenon_L93_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.85 apply (zenon_L51_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.85 apply (zenon_L379_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.85 apply (zenon_L243_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.85 apply (zenon_L94_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.85 apply (zenon_L380_); trivial. % 5.66/5.85 apply (zenon_L284_); trivial. % 5.66/5.85 apply (zenon_L433_); trivial. % 5.66/5.85 (* end of lemma zenon_L434_ *) % 5.66/5.85 assert (zenon_L435_ : (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e1)) = (e1)) -> ((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)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.66/5.85 do 0 intro. intros zenon_Hb7 zenon_Hb8 zenon_H42 zenon_Hb0 zenon_H8e zenon_H9d zenon_H41 zenon_H26 zenon_H86 zenon_H73 zenon_H14b. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.85 exact (zenon_Hb8 zenon_Hba). % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.85 apply (zenon_L102_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.85 apply (zenon_L45_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.85 apply (zenon_L99_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.85 exact (zenon_H26 zenon_H2d). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.85 apply (zenon_L26_); trivial. % 5.66/5.85 apply (zenon_L392_); trivial. % 5.66/5.85 (* end of lemma zenon_L435_ *) % 5.66/5.85 assert (zenon_L436_ : ((op (e2) (e3)) = (e0)) -> ((op (e2) (e3)) = (e1)) -> (~((e0) = (e1))) -> False). % 5.66/5.85 do 0 intro. intros zenon_H65 zenon_H144 zenon_Hee. % 5.66/5.85 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H12c | zenon_intro zenon_H94 ]. % 5.66/5.85 cut (((e1) = (e1)) = ((e0) = (e1))). % 5.66/5.85 intro zenon_D_pnotp. % 5.66/5.85 apply zenon_Hee. % 5.66/5.85 rewrite <- zenon_D_pnotp. % 5.66/5.85 exact zenon_H12c. % 5.66/5.85 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.85 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 5.66/5.85 congruence. % 5.66/5.85 cut (((op (e2) (e3)) = (e0)) = ((e1) = (e0))). % 5.66/5.85 intro zenon_D_pnotp. % 5.66/5.85 apply zenon_H12d. % 5.66/5.85 rewrite <- zenon_D_pnotp. % 5.66/5.85 exact zenon_H65. % 5.66/5.85 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.85 cut (((op (e2) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 5.66/5.85 congruence. % 5.66/5.85 exact (zenon_H145 zenon_H144). % 5.66/5.85 apply zenon_H67. apply refl_equal. % 5.66/5.85 apply zenon_H94. apply refl_equal. % 5.66/5.85 apply zenon_H94. apply refl_equal. % 5.66/5.85 (* end of lemma zenon_L436_ *) % 5.66/5.85 assert (zenon_L437_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))) -> ((op (e3) (e3)) = (e1)) -> False). % 5.66/5.85 do 0 intro. intros zenon_H1f3 zenon_H5f. % 5.66/5.85 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 5.66/5.85 cut (((op (e3) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H58]. % 5.66/5.85 congruence. % 5.66/5.85 exact (zenon_H58 zenon_H5f). % 5.66/5.85 exact (zenon_H58 zenon_H5f). % 5.66/5.85 (* end of lemma zenon_L437_ *) % 5.66/5.85 assert (zenon_L438_ : ((op (e0) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> ((op (e3) (e3)) = (e1)) -> False). % 5.66/5.85 do 0 intro. intros zenon_H167 zenon_H28 zenon_H5f. % 5.66/5.85 apply (zenon_notand_s _ _ ax12); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1f4 ]. % 5.66/5.85 apply zenon_H1aa. apply sym_equal. exact zenon_H5f. % 5.66/5.85 apply (zenon_notand_s _ _ zenon_H1f4); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H1f5 ]. % 5.66/5.85 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.85 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e0) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.85 intro zenon_D_pnotp. % 5.66/5.85 apply zenon_H1b5. % 5.66/5.85 rewrite <- zenon_D_pnotp. % 5.66/5.85 exact zenon_H1b6. % 5.66/5.85 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.85 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 5.66/5.85 congruence. % 5.66/5.85 cut (((op (e1) (e1)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 5.66/5.85 intro zenon_D_pnotp. % 5.66/5.85 apply zenon_H1b8. % 5.66/5.85 rewrite <- zenon_D_pnotp. % 5.66/5.85 exact zenon_H28. % 5.66/5.85 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.85 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 5.66/5.85 congruence. % 5.66/5.85 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.85 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.85 intro zenon_D_pnotp. % 5.66/5.85 apply zenon_H1f6. % 5.66/5.85 rewrite <- zenon_D_pnotp. % 5.66/5.85 exact zenon_H1b6. % 5.66/5.85 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.85 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 5.66/5.85 congruence. % 5.66/5.85 apply (zenon_L437_); trivial. % 5.66/5.85 apply zenon_H1b7. apply refl_equal. % 5.66/5.85 apply zenon_H1b7. apply refl_equal. % 5.66/5.85 apply zenon_H67. apply refl_equal. % 5.66/5.85 apply zenon_H1b7. apply refl_equal. % 5.66/5.85 apply zenon_H1b7. apply refl_equal. % 5.66/5.85 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.66/5.85 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.66/5.85 intro zenon_D_pnotp. % 5.66/5.85 apply zenon_H1f5. % 5.66/5.85 rewrite <- zenon_D_pnotp. % 5.66/5.85 exact zenon_H1ba. % 5.66/5.85 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.66/5.85 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 5.66/5.85 congruence. % 5.66/5.85 cut (((op (e0) (e3)) = (e2)) = ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e2))). % 5.66/5.85 intro zenon_D_pnotp. % 5.66/5.85 apply zenon_H1f7. % 5.66/5.85 rewrite <- zenon_D_pnotp. % 5.66/5.85 exact zenon_H167. % 5.66/5.85 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.85 cut (((op (e0) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bd]. % 5.66/5.85 congruence. % 5.66/5.85 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.66/5.85 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((op (e0) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.66/5.85 intro zenon_D_pnotp. % 5.66/5.85 apply zenon_H1bd. % 5.66/5.85 rewrite <- zenon_D_pnotp. % 5.66/5.85 exact zenon_H1ba. % 5.66/5.85 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.66/5.85 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (e0) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 5.66/5.85 congruence. % 5.66/5.85 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.85 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 5.66/5.85 congruence. % 5.66/5.85 cut (((op (e1) (e1)) = (e0)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e0))). % 5.66/5.85 intro zenon_D_pnotp. % 5.66/5.85 apply zenon_H1b8. % 5.66/5.85 rewrite <- zenon_D_pnotp. % 5.66/5.85 exact zenon_H28. % 5.66/5.85 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.85 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 5.66/5.85 congruence. % 5.66/5.85 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.85 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.85 intro zenon_D_pnotp. % 5.66/5.85 apply zenon_H1f6. % 5.66/5.85 rewrite <- zenon_D_pnotp. % 5.66/5.85 exact zenon_H1b6. % 5.66/5.85 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.85 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 5.66/5.85 congruence. % 5.66/5.85 apply (zenon_L437_); trivial. % 5.66/5.85 apply zenon_H1b7. apply refl_equal. % 5.66/5.85 apply zenon_H1b7. apply refl_equal. % 5.66/5.85 apply zenon_H67. apply refl_equal. % 5.66/5.85 apply zenon_H6f. apply refl_equal. % 5.66/5.85 apply zenon_H1bb. apply refl_equal. % 5.66/5.85 apply zenon_H1bb. apply refl_equal. % 5.66/5.85 apply zenon_H62. apply refl_equal. % 5.66/5.85 apply zenon_H1bb. apply refl_equal. % 5.66/5.85 apply zenon_H1bb. apply refl_equal. % 5.66/5.85 (* end of lemma zenon_L438_ *) % 5.66/5.85 assert (zenon_L439_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e1))) -> ((op (e0) (e3)) = (e2)) -> ((op (e1) (e1)) = (e0)) -> False). % 5.66/5.85 do 0 intro. intros zenon_H18e zenon_H6d zenon_H108 zenon_Ha6 zenon_H86 zenon_H63 zenon_H25 zenon_H42 zenon_H1d1 zenon_H4b zenon_H171 zenon_H97 zenon_H9d zenon_H89 zenon_Hee zenon_H167 zenon_H28. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H18f ]. % 5.66/5.85 apply (zenon_L100_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H12f | zenon_intro zenon_H190 ]. % 5.66/5.85 apply (zenon_L351_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H4f | zenon_intro zenon_H65 ]. % 5.66/5.85 exact (zenon_H4b zenon_H4f). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H14a | zenon_intro zenon_H172 ]. % 5.66/5.85 apply (zenon_L321_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_H173 ]. % 5.66/5.85 apply (zenon_L345_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H144 | zenon_intro zenon_H5f ]. % 5.66/5.85 apply (zenon_L436_); trivial. % 5.66/5.85 apply (zenon_L438_); trivial. % 5.66/5.85 (* end of lemma zenon_L439_ *) % 5.66/5.85 assert (zenon_L440_ : (((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) (e3)) = (e2)) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e0) (e1)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> ((op (e2) (e0)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 5.66/5.85 do 0 intro. intros zenon_H17d zenon_H1f zenon_H191 zenon_H167 zenon_Hee zenon_H9d zenon_H171 zenon_H4b zenon_H1d1 zenon_H42 zenon_Ha6 zenon_H108 zenon_H18e zenon_H86 zenon_H63 zenon_H25 zenon_H41 zenon_H97 zenon_H105 zenon_H6d zenon_H89. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.85 apply (zenon_L246_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.85 apply (zenon_L439_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.85 apply (zenon_L399_); trivial. % 5.66/5.85 apply (zenon_L301_); trivial. % 5.66/5.85 (* end of lemma zenon_L440_ *) % 5.66/5.85 assert (zenon_L441_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (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))) -> (~((e0) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((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) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e2)) = (e2)) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e3) (e3)) = (e3))) -> False). % 5.66/5.85 do 0 intro. intros zenon_H14f zenon_H150 zenon_H18e zenon_H1f zenon_H18c zenon_Hc2 zenon_H63 zenon_H6d zenon_H143 zenon_H129 zenon_H1c7 zenon_H16a zenon_H97 zenon_H41 zenon_H110 zenon_H86 zenon_H9a zenon_H116 zenon_H45 zenon_H32 zenon_H18a zenon_Hde zenon_H8e zenon_H73 zenon_Haa zenon_H26 zenon_H17d zenon_H191 zenon_Hee zenon_H9d zenon_H171 zenon_H1d1 zenon_H25 zenon_H105 zenon_Hb8 zenon_H10a zenon_Hb7 zenon_H14b zenon_H169 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.85 exact (zenon_H150 zenon_H152). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.85 exact (zenon_H16a zenon_H16c). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.85 apply (zenon_L155_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.85 apply (zenon_L435_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.85 exact (zenon_Hb8 zenon_Hba). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.85 apply (zenon_L99_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.85 apply (zenon_L99_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.85 exact (zenon_H26 zenon_H2d). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.85 apply (zenon_L26_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hab ]. % 5.66/5.85 apply (zenon_L102_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H2d | zenon_intro zenon_Hac ]. % 5.66/5.85 exact (zenon_H26 zenon_H2d). % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha6 ]. % 5.66/5.85 apply (zenon_L114_); trivial. % 5.66/5.85 apply (zenon_L440_); trivial. % 5.66/5.85 apply (zenon_L389_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.85 apply (zenon_L133_); trivial. % 5.66/5.85 apply (zenon_L292_); trivial. % 5.66/5.85 (* end of lemma zenon_L441_ *) % 5.66/5.85 assert (zenon_L442_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e0) (e3)) = (op (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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((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))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e3) (e1)) = (e3)) -> ((op (e0) (e1)) = (e1)) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((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 (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 5.66/5.85 do 0 intro. intros zenon_H169 zenon_H16a zenon_H14b zenon_H123 zenon_Hb7 zenon_H10a zenon_Hb8 zenon_H89 zenon_H6d zenon_H105 zenon_H97 zenon_H41 zenon_H25 zenon_H63 zenon_H86 zenon_H18e zenon_Ha6 zenon_H42 zenon_H1d1 zenon_H4b zenon_H171 zenon_H9d zenon_Hee zenon_H191 zenon_H1f zenon_H17d zenon_Hcb zenon_H143. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.85 exact (zenon_H16a zenon_H16c). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.85 apply (zenon_L155_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.85 apply (zenon_L393_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.85 exact (zenon_Hb8 zenon_Hba). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.85 apply (zenon_L99_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.85 apply (zenon_L440_); trivial. % 5.66/5.85 apply (zenon_L307_); trivial. % 5.66/5.85 (* end of lemma zenon_L442_ *) % 5.66/5.85 assert (zenon_L443_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (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)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e3) (e1)) = (e3)) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e3) (e3)) = (e3))) -> False). % 5.66/5.85 do 0 intro. intros zenon_H14f zenon_H150 zenon_H143 zenon_Hcb zenon_H17d zenon_H1f zenon_H191 zenon_Hee zenon_H9d zenon_H171 zenon_H1d1 zenon_Ha6 zenon_H18e zenon_H86 zenon_H63 zenon_H25 zenon_H41 zenon_H97 zenon_H105 zenon_H6d zenon_H89 zenon_Hb8 zenon_H10a zenon_Hb7 zenon_H123 zenon_H14b zenon_H16a zenon_H169 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.85 exact (zenon_H150 zenon_H152). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.85 apply (zenon_L442_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.85 apply (zenon_L133_); trivial. % 5.66/5.85 apply (zenon_L292_); trivial. % 5.66/5.85 (* end of lemma zenon_L443_ *) % 5.66/5.85 assert (zenon_L444_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (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)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (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 (e3) (e3)) = (e3))) -> False). % 5.66/5.85 do 0 intro. intros zenon_H14f zenon_H150 zenon_H143 zenon_Hcb zenon_H17d zenon_H1f zenon_H191 zenon_Hee zenon_H9d zenon_H171 zenon_H1d1 zenon_H18e zenon_H86 zenon_H63 zenon_H25 zenon_H41 zenon_H97 zenon_H105 zenon_H6d zenon_Hb8 zenon_H10a zenon_Hb7 zenon_H123 zenon_H14b zenon_H16a zenon_H169 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.85 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.85 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.66/5.85 apply (zenon_L443_); trivial. % 5.66/5.85 (* end of lemma zenon_L444_ *) % 5.66/5.85 assert (zenon_L445_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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 (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((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 (e1) (e0)))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (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 (e0) (e0)) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e0)) = (e0)) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> False). % 5.66/5.85 do 0 intro. intros zenon_H1a5 zenon_Hde zenon_H1a0 zenon_H123 zenon_H105 zenon_H143 zenon_H126 zenon_H14f zenon_Hf7 zenon_Hb4 zenon_H55 zenon_H11f zenon_H4c zenon_H4d zenon_H4a zenon_H16a zenon_H97 zenon_Hb7 zenon_H14b zenon_H8e zenon_H86 zenon_Hb8 zenon_H10a zenon_H110 zenon_H1c7 zenon_H191 zenon_H6d zenon_H1d1 zenon_H63 zenon_H4b zenon_H171 zenon_Hee zenon_H18e zenon_H17d zenon_H169 zenon_H150 zenon_H9d zenon_Ha6 zenon_H9f zenon_H41 zenon_H38 zenon_H32 zenon_H21 zenon_H26 zenon_H25 zenon_H23 zenon_H1f zenon_Ha7 zenon_H195. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.85 apply (zenon_L1_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.85 apply (zenon_L3_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.85 apply (zenon_L5_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.85 apply (zenon_L7_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.85 apply (zenon_L8_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.85 apply (zenon_L9_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.85 apply (zenon_L106_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.85 apply (zenon_L295_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.85 apply (zenon_L242_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.85 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.66/5.85 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.85 exact (zenon_H150 zenon_H152). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.85 exact (zenon_H16a zenon_H16c). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.85 apply (zenon_L155_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.85 apply (zenon_L435_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.85 exact (zenon_Hb8 zenon_Hba). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.85 apply (zenon_L99_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.85 apply (zenon_L246_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.85 apply (zenon_L99_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.85 exact (zenon_H26 zenon_H2d). % 5.66/5.85 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.85 apply (zenon_L26_); trivial. % 5.66/5.85 apply (zenon_L439_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.85 apply (zenon_L21_); trivial. % 5.66/5.85 apply (zenon_L405_); trivial. % 5.66/5.85 apply (zenon_L335_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.85 apply (zenon_L133_); trivial. % 5.66/5.85 apply (zenon_L292_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.85 apply (zenon_L51_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.85 apply (zenon_L331_); trivial. % 5.66/5.85 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.86 apply (zenon_L299_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.66/5.86 apply (zenon_L443_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.86 apply (zenon_L303_); trivial. % 5.66/5.86 apply (zenon_L284_); trivial. % 5.66/5.86 apply (zenon_L42_); trivial. % 5.66/5.86 apply (zenon_L280_); trivial. % 5.66/5.86 (* end of lemma zenon_L445_ *) % 5.66/5.86 assert (zenon_L446_ : (((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)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 5.66/5.86 do 0 intro. intros zenon_H105 zenon_H97 zenon_H41 zenon_H25 zenon_H45 zenon_H52 zenon_H86 zenon_H89. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.66/5.86 apply (zenon_L333_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.66/5.86 exact (zenon_H25 zenon_H2e). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.66/5.86 apply (zenon_L74_); trivial. % 5.66/5.86 apply (zenon_L398_); trivial. % 5.66/5.86 (* end of lemma zenon_L446_ *) % 5.66/5.86 assert (zenon_L447_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> (((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)) -> (~((e2) = (e3))) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hcb zenon_H105 zenon_H97 zenon_H41 zenon_H25 zenon_H45 zenon_H52 zenon_H86. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.66/5.86 apply (zenon_L446_); trivial. % 5.66/5.86 (* end of lemma zenon_L447_ *) % 5.66/5.86 assert (zenon_L448_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e0) (e0)) = (e0)) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hde zenon_H18a zenon_H38 zenon_H9a zenon_H11f zenon_Hd9 zenon_H1ad zenon_H1f zenon_H86 zenon_H45 zenon_H25 zenon_H41 zenon_H97 zenon_H105 zenon_H52. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.86 apply (zenon_L1_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.86 apply (zenon_L238_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.86 apply (zenon_L58_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.86 apply (zenon_L7_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.86 apply (zenon_L8_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.86 apply (zenon_L9_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.86 apply (zenon_L59_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.86 apply (zenon_L332_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.86 apply (zenon_L190_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.86 apply (zenon_L61_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.86 apply (zenon_L62_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.86 apply (zenon_L310_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.86 apply (zenon_L243_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.86 apply (zenon_L447_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.86 apply (zenon_L63_); trivial. % 5.66/5.86 apply (zenon_L284_); trivial. % 5.66/5.86 (* end of lemma zenon_L448_ *) % 5.66/5.86 assert (zenon_L449_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e0) (e1)) = (e0)) -> False). % 5.66/5.86 do 0 intro. intros zenon_H3b zenon_Hed zenon_H22. % 5.66/5.86 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.66/5.86 apply (zenon_L66_); trivial. % 5.66/5.86 (* end of lemma zenon_L449_ *) % 5.66/5.86 assert (zenon_L450_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> ((op (e1) (e2)) = (e2)) -> ((op (e0) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.66/5.86 do 0 intro. intros zenon_H8e zenon_H6d zenon_H31 zenon_H26 zenon_H86 zenon_H73 zenon_Hb3 zenon_H14b. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.86 apply (zenon_L19_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.86 exact (zenon_H26 zenon_H2d). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.86 apply (zenon_L26_); trivial. % 5.66/5.86 apply (zenon_L392_); trivial. % 5.66/5.86 (* end of lemma zenon_L450_ *) % 5.66/5.86 assert (zenon_L451_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e2) (e3)) = (e0)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 5.66/5.86 do 0 intro. intros zenon_H55 zenon_H65 zenon_Hce zenon_H58 zenon_H59 zenon_H3e. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 5.66/5.86 cut (((op (e2) (e3)) = (e0)) = ((op (e2) (e3)) = (op (e3) (e3)))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_Hce. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H65. % 5.66/5.86 cut (((e0) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 5.66/5.86 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 5.66/5.86 congruence. % 5.66/5.86 apply zenon_H176. apply refl_equal. % 5.66/5.86 apply zenon_H5c. apply sym_equal. exact zenon_H5b. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 5.66/5.86 exact (zenon_H58 zenon_H5f). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 5.66/5.86 exact (zenon_H59 zenon_H61). % 5.66/5.86 exact (zenon_H3e zenon_H60). % 5.66/5.86 (* end of lemma zenon_L451_ *) % 5.66/5.86 assert (zenon_L452_ : (~((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))) -> ((op (e3) (e3)) = (e0)) -> False). % 5.66/5.86 do 0 intro. intros zenon_H1f8 zenon_H5b. % 5.66/5.86 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 5.66/5.86 cut (((op (e3) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 5.66/5.86 congruence. % 5.66/5.86 exact (zenon_Hf7 zenon_H5b). % 5.66/5.86 exact (zenon_Hf7 zenon_H5b). % 5.66/5.86 (* end of lemma zenon_L452_ *) % 5.66/5.86 assert (zenon_L453_ : ((op (e1) (e3)) = (e2)) -> ((op (e0) (e0)) = (e1)) -> ((op (e3) (e3)) = (e0)) -> False). % 5.66/5.86 do 0 intro. intros zenon_H96 zenon_H152 zenon_H5b. % 5.66/5.86 apply (zenon_notand_s _ _ ax6); [ zenon_intro zenon_H5c | zenon_intro zenon_H1f9 ]. % 5.66/5.86 apply zenon_H5c. apply sym_equal. exact zenon_H5b. % 5.66/5.86 apply (zenon_notand_s _ _ zenon_H1f9); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1f5 ]. % 5.66/5.86 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.86 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e1) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H1fa. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H1b6. % 5.66/5.86 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.86 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 5.66/5.86 congruence. % 5.66/5.86 cut (((op (e0) (e0)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H1fb. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H152. % 5.66/5.86 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.86 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 5.66/5.86 congruence. % 5.66/5.86 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.86 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H1fc. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H1b6. % 5.66/5.86 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.86 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 5.66/5.86 congruence. % 5.66/5.86 apply (zenon_L452_); trivial. % 5.66/5.86 apply zenon_H1b7. apply refl_equal. % 5.66/5.86 apply zenon_H1b7. apply refl_equal. % 5.66/5.86 apply zenon_H94. apply refl_equal. % 5.66/5.86 apply zenon_H1b7. apply refl_equal. % 5.66/5.86 apply zenon_H1b7. apply refl_equal. % 5.66/5.86 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.66/5.86 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((e2) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H1f5. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H1ba. % 5.66/5.86 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.66/5.86 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1f7]. % 5.66/5.86 congruence. % 5.66/5.86 cut (((op (e1) (e3)) = (e2)) = ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e2))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H1f7. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H96. % 5.66/5.86 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.86 cut (((op (e1) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 5.66/5.86 congruence. % 5.66/5.86 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.66/5.86 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((op (e1) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H1fd. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H1ba. % 5.66/5.86 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.66/5.86 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1fe]. % 5.66/5.86 congruence. % 5.66/5.86 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.86 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 5.66/5.86 congruence. % 5.66/5.86 cut (((op (e0) (e0)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H1fb. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H152. % 5.66/5.86 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.86 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 5.66/5.86 congruence. % 5.66/5.86 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.86 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H1fc. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H1b6. % 5.66/5.86 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.86 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 5.66/5.86 congruence. % 5.66/5.86 apply (zenon_L452_); trivial. % 5.66/5.86 apply zenon_H1b7. apply refl_equal. % 5.66/5.86 apply zenon_H1b7. apply refl_equal. % 5.66/5.86 apply zenon_H94. apply refl_equal. % 5.66/5.86 apply zenon_H6f. apply refl_equal. % 5.66/5.86 apply zenon_H1bb. apply refl_equal. % 5.66/5.86 apply zenon_H1bb. apply refl_equal. % 5.66/5.86 apply zenon_H62. apply refl_equal. % 5.66/5.86 apply zenon_H1bb. apply refl_equal. % 5.66/5.86 apply zenon_H1bb. apply refl_equal. % 5.66/5.86 (* end of lemma zenon_L453_ *) % 5.66/5.86 assert (zenon_L454_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e3)) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (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) (e0)) = (e1)) -> False). % 5.66/5.86 do 0 intro. intros zenon_H105 zenon_H63 zenon_H25 zenon_H14b zenon_H86 zenon_H26 zenon_H31 zenon_H8e zenon_Hf8 zenon_H6d zenon_Hb3 zenon_H57 zenon_H3e zenon_H59 zenon_H58 zenon_Hce zenon_H55 zenon_H152. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.66/5.86 apply (zenon_L18_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.66/5.86 exact (zenon_H25 zenon_H2e). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.66/5.86 apply (zenon_L450_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H3d | zenon_intro zenon_Hfb ]. % 5.66/5.86 apply (zenon_L271_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H56 | zenon_intro zenon_Hfc ]. % 5.66/5.86 apply (zenon_L13_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H65 | zenon_intro zenon_H5b ]. % 5.66/5.86 apply (zenon_L451_); trivial. % 5.66/5.86 apply (zenon_L453_); trivial. % 5.66/5.86 (* end of lemma zenon_L454_ *) % 5.66/5.86 assert (zenon_L455_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e0) (e0)) = (e1)) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 5.66/5.86 do 0 intro. intros zenon_H17d zenon_H152 zenon_Hce zenon_Hb3 zenon_H6d zenon_Hf8 zenon_H8e zenon_H26 zenon_H86 zenon_H14b zenon_H25 zenon_H63 zenon_H105 zenon_H13f zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H55 zenon_H57 zenon_H58 zenon_H59 zenon_H3e. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.86 apply (zenon_L454_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.86 exact (zenon_H13f zenon_H28). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.86 apply (zenon_L179_); trivial. % 5.66/5.86 apply (zenon_L13_); trivial. % 5.66/5.86 (* end of lemma zenon_L455_ *) % 5.66/5.86 assert (zenon_L456_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (((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 (e3) (e3)) = (e3))) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hbc zenon_H14f zenon_H58 zenon_H57 zenon_H4a zenon_H45 zenon_H77 zenon_H4c zenon_H4d zenon_H13f zenon_H105 zenon_H63 zenon_H25 zenon_H14b zenon_H86 zenon_H26 zenon_H8e zenon_Hf8 zenon_H6d zenon_Hce zenon_H17d zenon_Hb8 zenon_Hb7 zenon_Hee zenon_H22 zenon_H97 zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.86 exact (zenon_Hb8 zenon_Hba). % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.86 apply (zenon_L40_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.86 apply (zenon_L45_); trivial. % 5.66/5.86 apply (zenon_L455_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.86 apply (zenon_L154_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.86 apply (zenon_L156_); trivial. % 5.66/5.86 apply (zenon_L292_); trivial. % 5.66/5.86 (* end of lemma zenon_L456_ *) % 5.66/5.86 assert (zenon_L457_ : (((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)) = (e1)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 5.66/5.86 do 0 intro. intros zenon_H169 zenon_H16a zenon_H63 zenon_H22 zenon_H149 zenon_H97 zenon_H86 zenon_Hb3. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.86 exact (zenon_H16a zenon_H16c). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.86 apply (zenon_L357_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.86 apply (zenon_L156_); trivial. % 5.66/5.86 apply (zenon_L401_); trivial. % 5.66/5.86 (* end of lemma zenon_L457_ *) % 5.66/5.86 assert (zenon_L458_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((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 (e3) (e3)) = (e3))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((e0) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 5.66/5.86 do 0 intro. intros zenon_H14f zenon_H55 zenon_Hce zenon_H58 zenon_H59 zenon_H3e zenon_H57 zenon_H6d zenon_Hf8 zenon_H8e zenon_H31 zenon_H26 zenon_H14b zenon_H25 zenon_H105 zenon_Hee zenon_H86 zenon_H97 zenon_H22 zenon_H63 zenon_H16a zenon_H169 zenon_H9d zenon_Hb3. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.86 apply (zenon_L454_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.86 apply (zenon_L154_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.86 apply (zenon_L457_); trivial. % 5.66/5.86 apply (zenon_L272_); trivial. % 5.66/5.86 (* end of lemma zenon_L458_ *) % 5.66/5.86 assert (zenon_L459_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e3) (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_Hb3 zenon_H9d zenon_H169 zenon_H16a zenon_H22 zenon_H97 zenon_H86 zenon_Hee zenon_H105 zenon_H25 zenon_H14b zenon_H26 zenon_H8e zenon_Hf8 zenon_H57 zenon_H3e zenon_H59 zenon_H58 zenon_Hce zenon_H55 zenon_H14f zenon_Hbe zenon_H63 zenon_H6d zenon_Hca. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.66/5.86 exact (zenon_H20 zenon_H1f). % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.66/5.86 apply (zenon_L458_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.66/5.86 apply (zenon_L320_); trivial. % 5.66/5.86 apply (zenon_L304_); trivial. % 5.66/5.86 (* end of lemma zenon_L459_ *) % 5.66/5.86 assert (zenon_L460_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (((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 (e3) (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 (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((e1) = (e2))) -> ((op (e2) (e0)) = (e2)) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hde zenon_H72 zenon_Hed zenon_H118 zenon_H188 zenon_Hb4 zenon_Hf7 zenon_Hb7 zenon_Hb8 zenon_H17d zenon_H13f zenon_H4d zenon_H4c zenon_H45 zenon_H4a zenon_Hf0 zenon_H6d zenon_H63 zenon_H14f zenon_H55 zenon_Hce zenon_H58 zenon_H59 zenon_H3e zenon_H57 zenon_Hf8 zenon_H8e zenon_H26 zenon_H14b zenon_H25 zenon_H105 zenon_Hee zenon_H86 zenon_H22 zenon_H16a zenon_H169 zenon_Hf6 zenon_H9d zenon_H77 zenon_H11a zenon_H2c zenon_H97 zenon_Hbe zenon_H146. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.86 apply (zenon_L16_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.86 apply (zenon_L87_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.86 apply (zenon_L31_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.86 apply (zenon_L449_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.86 apply (zenon_L89_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.86 apply (zenon_L90_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.86 apply (zenon_L92_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.86 apply (zenon_L421_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.86 apply (zenon_L456_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.86 apply (zenon_L93_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.86 apply (zenon_L51_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.86 apply (zenon_L329_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.66/5.86 apply (zenon_L459_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.86 apply (zenon_L94_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.86 apply (zenon_L432_); trivial. % 5.66/5.86 apply (zenon_L284_); trivial. % 5.66/5.86 (* end of lemma zenon_L460_ *) % 5.66/5.86 assert (zenon_L461_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e3)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.86 do 0 intro. intros zenon_H171 zenon_Hee zenon_H2c zenon_H188 zenon_H59 zenon_H97 zenon_H86 zenon_H89 zenon_H3d zenon_H63 zenon_H1bf zenon_H58. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H14a | zenon_intro zenon_H172 ]. % 5.66/5.86 apply (zenon_L161_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_H173 ]. % 5.66/5.86 apply (zenon_L217_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H144 | zenon_intro zenon_H5f ]. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H167 | zenon_intro zenon_H1c0 ]. % 5.66/5.86 apply (zenon_L163_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H96 | zenon_intro zenon_H1c1 ]. % 5.66/5.86 apply (zenon_L398_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H64 | zenon_intro zenon_H61 ]. % 5.66/5.86 apply (zenon_L129_); trivial. % 5.66/5.86 exact (zenon_H59 zenon_H61). % 5.66/5.86 exact (zenon_H58 zenon_H5f). % 5.66/5.86 (* end of lemma zenon_L461_ *) % 5.66/5.86 assert (zenon_L462_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e0)) = (e3)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 5.66/5.86 do 0 intro. intros zenon_H8e zenon_H6d zenon_H31 zenon_H26 zenon_H4d zenon_H4c zenon_H77 zenon_Hba zenon_H4a zenon_H9d zenon_H97 zenon_Hb0 zenon_H163 zenon_H86 zenon_H96. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.86 apply (zenon_L19_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.86 exact (zenon_H26 zenon_H2d). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.86 apply (zenon_L177_); trivial. % 5.66/5.86 apply (zenon_L398_); trivial. % 5.66/5.86 (* end of lemma zenon_L462_ *) % 5.66/5.86 assert (zenon_L463_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (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))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_H3e zenon_H59 zenon_Hb4 zenon_Hf7 zenon_H55 zenon_H97 zenon_Hb0 zenon_Hb7 zenon_H163 zenon_H26 zenon_H8e zenon_H171 zenon_Hee zenon_H2c zenon_H188 zenon_H1bf zenon_H58 zenon_H25 zenon_H105 zenon_H9d zenon_H86 zenon_H6d zenon_H150 zenon_H14f zenon_Hbe zenon_H63 zenon_H17d zenon_H122 zenon_H13f zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H14b zenon_H3d. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.66/5.86 exact (zenon_H20 zenon_H1f). % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.86 exact (zenon_H150 zenon_H152). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.66/5.86 apply (zenon_L18_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.66/5.86 exact (zenon_H25 zenon_H2e). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.86 apply (zenon_L19_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.86 exact (zenon_H26 zenon_H2d). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.86 apply (zenon_L26_); trivial. % 5.66/5.86 apply (zenon_L461_); trivial. % 5.66/5.86 apply (zenon_L462_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.86 apply (zenon_L102_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.86 apply (zenon_L45_); trivial. % 5.66/5.86 apply (zenon_L271_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.86 apply (zenon_L156_); trivial. % 5.66/5.86 apply (zenon_L292_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.66/5.86 apply (zenon_L320_); trivial. % 5.66/5.86 apply (zenon_L314_); trivial. % 5.66/5.86 (* end of lemma zenon_L463_ *) % 5.66/5.86 assert (zenon_L464_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (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) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (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))))) -> (~((e1) = (e2))) -> ((op (e0) (e2)) = (e2)) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.66/5.86 do 0 intro. intros zenon_H16e zenon_H146 zenon_H11a zenon_H169 zenon_H16a zenon_Hf8 zenon_H57 zenon_Hce zenon_Hb8 zenon_H118 zenon_Hed zenon_H72 zenon_Hde zenon_H116 zenon_Hf0 zenon_H11f zenon_H113 zenon_H117 zenon_Hf6 zenon_H20 zenon_H3e zenon_H59 zenon_Hb4 zenon_Hf7 zenon_H55 zenon_H97 zenon_Hb0 zenon_Hb7 zenon_H163 zenon_H26 zenon_H8e zenon_H171 zenon_Hee zenon_H2c zenon_H188 zenon_H1bf zenon_H58 zenon_H25 zenon_H105 zenon_H9d zenon_H86 zenon_H6d zenon_H150 zenon_H14f zenon_Hbe zenon_H63 zenon_H17d zenon_H122 zenon_H13f zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H14b. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.66/5.86 exact (zenon_H20 zenon_H1f). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.66/5.86 apply (zenon_L460_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.66/5.86 apply (zenon_L108_); trivial. % 5.66/5.86 apply (zenon_L463_); trivial. % 5.66/5.86 (* end of lemma zenon_L464_ *) % 5.66/5.86 assert (zenon_L465_ : (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e1) (e2)) = (e2)) -> ((op (e3) (e2)) = (e2)) -> False). % 5.66/5.86 do 0 intro. intros zenon_H1ef zenon_H73 zenon_Hc7. % 5.66/5.86 cut (((op (e1) (e2)) = (e2)) = ((op (e1) (e2)) = (op (e3) (e2)))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H1ef. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H73. % 5.66/5.86 cut (((e2) = (op (e3) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 5.66/5.86 cut (((op (e1) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H49]. % 5.66/5.86 congruence. % 5.66/5.86 apply zenon_H49. apply refl_equal. % 5.66/5.86 apply zenon_H19e. apply sym_equal. exact zenon_Hc7. % 5.66/5.86 (* end of lemma zenon_L465_ *) % 5.66/5.86 assert (zenon_L466_ : ((op (e2) (e3)) = (e2)) -> ((op (e1) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 5.66/5.86 do 0 intro. intros zenon_H64 zenon_H96 zenon_H1ff. % 5.66/5.86 elim (classic ((op (e2) (e3)) = (op (e2) (e3)))); [ zenon_intro zenon_H175 | zenon_intro zenon_H176 ]. % 5.66/5.86 cut (((op (e2) (e3)) = (op (e2) (e3))) = ((op (e1) (e3)) = (op (e2) (e3)))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H1ff. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H175. % 5.66/5.86 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 5.66/5.86 cut (((op (e2) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H200]. % 5.66/5.86 congruence. % 5.66/5.86 cut (((op (e2) (e3)) = (e2)) = ((op (e2) (e3)) = (op (e1) (e3)))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H200. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H64. % 5.66/5.86 cut (((e2) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 5.66/5.86 cut (((op (e2) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 5.66/5.86 congruence. % 5.66/5.86 apply zenon_H176. apply refl_equal. % 5.66/5.86 apply zenon_H201. apply sym_equal. exact zenon_H96. % 5.66/5.86 apply zenon_H176. apply refl_equal. % 5.66/5.86 apply zenon_H176. apply refl_equal. % 5.66/5.86 (* end of lemma zenon_L466_ *) % 5.66/5.86 assert (zenon_L467_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> False). % 5.66/5.86 do 0 intro. intros zenon_H105 zenon_H63 zenon_H31 zenon_H25 zenon_Hc7 zenon_H1ef zenon_H64 zenon_H1ff. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.66/5.86 apply (zenon_L18_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.66/5.86 exact (zenon_H25 zenon_H2e). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.66/5.86 apply (zenon_L465_); trivial. % 5.66/5.86 apply (zenon_L466_); trivial. % 5.66/5.86 (* end of lemma zenon_L467_ *) % 5.66/5.86 assert (zenon_L468_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e1)) -> (~((e0) = (e1))) -> False). % 5.66/5.86 do 0 intro. intros zenon_H39 zenon_H182 zenon_Hee. % 5.66/5.86 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H12c | zenon_intro zenon_H94 ]. % 5.66/5.86 cut (((e1) = (e1)) = ((e0) = (e1))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_Hee. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H12c. % 5.66/5.86 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.86 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 5.66/5.86 congruence. % 5.66/5.86 cut (((op (e3) (e0)) = (e0)) = ((e1) = (e0))). % 5.66/5.86 intro zenon_D_pnotp. % 5.66/5.86 apply zenon_H12d. % 5.66/5.86 rewrite <- zenon_D_pnotp. % 5.66/5.86 exact zenon_H39. % 5.66/5.86 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.86 cut (((op (e3) (e0)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 5.66/5.86 congruence. % 5.66/5.86 exact (zenon_H1ca zenon_H182). % 5.66/5.86 apply zenon_H67. apply refl_equal. % 5.66/5.86 apply zenon_H94. apply refl_equal. % 5.66/5.86 apply zenon_H94. apply refl_equal. % 5.66/5.86 (* end of lemma zenon_L468_ *) % 5.66/5.86 assert (zenon_L469_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.86 do 0 intro. intros zenon_H185 zenon_Hee zenon_H39 zenon_H2c zenon_H1f2 zenon_Hc7 zenon_H97 zenon_H58. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H182 | zenon_intro zenon_H186 ]. % 5.66/5.86 apply (zenon_L468_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Haf | zenon_intro zenon_H187 ]. % 5.66/5.86 apply (zenon_L424_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H15e | zenon_intro zenon_H5f ]. % 5.66/5.86 apply (zenon_L363_); trivial. % 5.66/5.86 exact (zenon_H58 zenon_H5f). % 5.66/5.86 (* end of lemma zenon_L469_ *) % 5.66/5.86 assert (zenon_L470_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_H1ff zenon_H1ef zenon_H25 zenon_H63 zenon_H105 zenon_H64 zenon_H77 zenon_H11a zenon_H146 zenon_H185 zenon_Hee zenon_H2c zenon_H1f2 zenon_Hc7 zenon_H97 zenon_H58. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.66/5.86 exact (zenon_H20 zenon_H1f). % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.66/5.86 apply (zenon_L467_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.66/5.86 apply (zenon_L146_); trivial. % 5.66/5.86 apply (zenon_L469_); trivial. % 5.66/5.86 (* end of lemma zenon_L470_ *) % 5.66/5.86 assert (zenon_L471_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hc5 zenon_Hf6 zenon_H20 zenon_H1ff zenon_H1ef zenon_H25 zenon_H63 zenon_H105 zenon_H77 zenon_H11a zenon_H146 zenon_H185 zenon_Hee zenon_H2c zenon_H1f2 zenon_H97 zenon_H58. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.66/5.86 apply (zenon_L470_); trivial. % 5.66/5.86 (* end of lemma zenon_L471_ *) % 5.66/5.86 assert (zenon_L472_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hc5 zenon_Hf6 zenon_H20 zenon_H1ff zenon_H1ef zenon_H25 zenon_H63 zenon_H105 zenon_H77 zenon_H11a zenon_H146 zenon_H185 zenon_Hee zenon_H2c zenon_H1f2 zenon_H97 zenon_H58. % 5.66/5.86 apply (zenon_L471_); trivial. % 5.66/5.86 (* end of lemma zenon_L472_ *) % 5.66/5.86 assert (zenon_L473_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 5.66/5.86 do 0 intro. intros zenon_H14f zenon_H3e zenon_H59 zenon_H58 zenon_H57 zenon_H55 zenon_H4a zenon_H45 zenon_H77 zenon_H4c zenon_H4d zenon_H13f zenon_H105 zenon_H25 zenon_H14b zenon_H26 zenon_H8e zenon_Hf8 zenon_H6d zenon_Hce zenon_H17d zenon_Hee zenon_H86 zenon_H97 zenon_H22 zenon_H63 zenon_H16a zenon_H169 zenon_H9d zenon_Hb3. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.86 apply (zenon_L455_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.86 apply (zenon_L154_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.86 apply (zenon_L457_); trivial. % 5.66/5.86 apply (zenon_L272_); trivial. % 5.66/5.86 (* end of lemma zenon_L473_ *) % 5.66/5.86 assert (zenon_L474_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e1) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((e2) = (e3))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hc8 zenon_H16e zenon_H9d zenon_H169 zenon_H16a zenon_H63 zenon_H97 zenon_H86 zenon_Hee zenon_H17d zenon_Hce zenon_Hf8 zenon_H8e zenon_H26 zenon_H14b zenon_H25 zenon_H105 zenon_H13f zenon_H45 zenon_H55 zenon_H57 zenon_H58 zenon_H59 zenon_H3e zenon_H14f zenon_H4d zenon_H4c zenon_H77 zenon_H11f zenon_H4a zenon_H6d. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.66/5.86 exact (zenon_H20 zenon_H1f). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.66/5.86 apply (zenon_L473_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.66/5.86 apply (zenon_L98_); trivial. % 5.66/5.86 apply (zenon_L271_); trivial. % 5.66/5.86 (* end of lemma zenon_L474_ *) % 5.66/5.86 assert (zenon_L475_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.86 do 0 intro. intros zenon_H1d1 zenon_H63 zenon_H22 zenon_H25 zenon_H110 zenon_Hbc zenon_H86 zenon_Ha6. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H15a | zenon_intro zenon_H1d2 ]. % 5.66/5.86 apply (zenon_L357_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H2e | zenon_intro zenon_H1d3 ]. % 5.66/5.86 exact (zenon_H25 zenon_H2e). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1cf ]. % 5.66/5.86 apply (zenon_L117_); trivial. % 5.66/5.86 apply (zenon_L350_); trivial. % 5.66/5.86 (* end of lemma zenon_L475_ *) % 5.66/5.86 assert (zenon_L476_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hde zenon_H72 zenon_Hed zenon_H118 zenon_H11a zenon_H9d zenon_H86 zenon_H110 zenon_H25 zenon_H22 zenon_H63 zenon_H1d1 zenon_Hbe zenon_Hf0 zenon_H143 zenon_H2c zenon_Ha6 zenon_H1a0. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.86 apply (zenon_L16_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.86 apply (zenon_L87_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.86 apply (zenon_L31_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.86 apply (zenon_L449_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.86 apply (zenon_L89_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.86 apply (zenon_L90_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.86 apply (zenon_L92_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.86 apply (zenon_L295_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.86 apply (zenon_L475_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.86 apply (zenon_L93_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.86 apply (zenon_L51_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.86 apply (zenon_L329_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.86 apply (zenon_L299_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.86 apply (zenon_L94_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.86 apply (zenon_L303_); trivial. % 5.66/5.86 apply (zenon_L284_); trivial. % 5.66/5.86 (* end of lemma zenon_L476_ *) % 5.66/5.86 assert (zenon_L477_ : (((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))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((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 (e3) (e3)) = (e3))) -> False). % 5.66/5.86 do 0 intro. intros zenon_H14f zenon_H150 zenon_Ha6 zenon_H6d zenon_H1d1 zenon_H25 zenon_H63 zenon_H86 zenon_H13f zenon_Hde zenon_H72 zenon_Hed zenon_H118 zenon_H11a zenon_H9d zenon_H110 zenon_Hbe zenon_Hf0 zenon_H143 zenon_H2c zenon_H1a0 zenon_H140 zenon_Hb0 zenon_H97 zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.86 exact (zenon_H150 zenon_H152). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.66/5.86 apply (zenon_L476_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.66/5.86 exact (zenon_H13f zenon_H28). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.66/5.86 apply (zenon_L351_); trivial. % 5.66/5.86 apply (zenon_L287_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.86 apply (zenon_L156_); trivial. % 5.66/5.86 apply (zenon_L292_); trivial. % 5.66/5.86 (* end of lemma zenon_L477_ *) % 5.66/5.86 assert (zenon_L478_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (((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))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e2))) -> (((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 (e3) (e3)) = (e3))) -> False). % 5.66/5.86 do 0 intro. intros zenon_Hbc zenon_H14f zenon_H150 zenon_Ha6 zenon_H6d zenon_H1d1 zenon_H25 zenon_H63 zenon_H86 zenon_H13f zenon_Hde zenon_H72 zenon_Hed zenon_H118 zenon_H11a zenon_H9d zenon_H110 zenon_Hf0 zenon_H143 zenon_H2c zenon_H1a0 zenon_H140 zenon_H97 zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.66/5.86 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.66/5.86 apply (zenon_L477_); trivial. % 5.66/5.86 (* end of lemma zenon_L478_ *) % 5.66/5.86 assert (zenon_L479_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e0)) = (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). % 5.66/5.86 do 0 intro. intros zenon_H105 zenon_H63 zenon_H25 zenon_H14b zenon_Hb3 zenon_H86 zenon_H26 zenon_H31 zenon_H6d zenon_H8e zenon_H64 zenon_H1ff. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.66/5.86 apply (zenon_L18_); trivial. % 5.66/5.86 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.66/5.86 exact (zenon_H25 zenon_H2e). % 5.66/5.86 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.66/5.86 apply (zenon_L450_); trivial. % 5.66/5.86 apply (zenon_L466_); trivial. % 5.66/5.86 (* end of lemma zenon_L479_ *) % 5.66/5.87 assert (zenon_L480_ : ((op (e0) (e2)) = (e0)) -> ((op (e0) (e2)) = (e1)) -> (~((e0) = (e1))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H33 zenon_H149 zenon_Hee. % 5.66/5.87 elim (classic ((e1) = (e1))); [ zenon_intro zenon_H12c | zenon_intro zenon_H94 ]. % 5.66/5.87 cut (((e1) = (e1)) = ((e0) = (e1))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_Hee. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H12c. % 5.66/5.87 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.87 cut (((e1) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 5.66/5.87 congruence. % 5.66/5.87 cut (((op (e0) (e2)) = (e0)) = ((e1) = (e0))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H12d. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H33. % 5.66/5.87 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.87 cut (((op (e0) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 5.66/5.87 congruence. % 5.66/5.87 exact (zenon_H15c zenon_H149). % 5.66/5.87 apply zenon_H67. apply refl_equal. % 5.66/5.87 apply zenon_H94. apply refl_equal. % 5.66/5.87 apply zenon_H94. apply refl_equal. % 5.66/5.87 (* end of lemma zenon_L480_ *) % 5.66/5.87 assert (zenon_L481_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (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 (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H195 zenon_Ha7 zenon_H20 zenon_Hb7 zenon_H63 zenon_H25 zenon_H8e zenon_H14b zenon_H86 zenon_H26 zenon_H1ff zenon_H64 zenon_H105 zenon_H33 zenon_H6d zenon_Ha6 zenon_H123 zenon_Hb8 zenon_H146 zenon_H97 zenon_H77 zenon_H2c zenon_H11a zenon_Hee zenon_H14f zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H55 zenon_H13f zenon_H1d1 zenon_H143 zenon_H140 zenon_H150 zenon_Hf6. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.66/5.87 exact (zenon_H20 zenon_H1f). % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.87 exact (zenon_Hb8 zenon_Hba). % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.87 apply (zenon_L391_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.87 apply (zenon_L103_); trivial. % 5.66/5.87 apply (zenon_L479_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.66/5.87 apply (zenon_L146_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.87 exact (zenon_H150 zenon_H152). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.87 apply (zenon_L352_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.87 apply (zenon_L480_); trivial. % 5.66/5.87 apply (zenon_L292_); trivial. % 5.66/5.87 apply (zenon_L42_); trivial. % 5.66/5.87 (* end of lemma zenon_L481_ *) % 5.66/5.87 assert (zenon_L482_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e2) (e0)) = (e2)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H36 zenon_H63 zenon_Hbe. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_Hd6. zenon_intro zenon_H4c. % 5.66/5.87 apply (zenon_L320_); trivial. % 5.66/5.87 (* end of lemma zenon_L482_ *) % 5.66/5.87 assert (zenon_L483_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H3b zenon_H17d zenon_H122 zenon_H13f zenon_H4d zenon_H4c zenon_H77 zenon_H45 zenon_H4a zenon_H14b. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.66/5.87 apply (zenon_L314_); trivial. % 5.66/5.87 (* end of lemma zenon_L483_ *) % 5.66/5.87 assert (zenon_L484_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e3))) -> False). % 5.66/5.87 do 0 intro. intros zenon_Hc8 zenon_H3d zenon_H6d. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.66/5.87 apply (zenon_L271_); trivial. % 5.66/5.87 (* end of lemma zenon_L484_ *) % 5.66/5.87 assert (zenon_L485_ : (~((e1) = (e3))) -> ((op (e3) (e2)) = (e3)) -> ((op (e3) (e2)) = (e1)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H9d zenon_Hd3 zenon_H15e. % 5.66/5.87 cut (((op (e3) (e2)) = (e3)) = ((e1) = (e3))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H9d. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_Hd3. % 5.66/5.87 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.87 cut (((op (e3) (e2)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 5.66/5.87 congruence. % 5.66/5.87 exact (zenon_H1de zenon_H15e). % 5.66/5.87 apply zenon_H6f. apply refl_equal. % 5.66/5.87 (* end of lemma zenon_L485_ *) % 5.66/5.87 assert (zenon_L486_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H185 zenon_Hee zenon_H39 zenon_H2c zenon_H1f2 zenon_Hd3 zenon_H9d zenon_H58. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H182 | zenon_intro zenon_H186 ]. % 5.66/5.87 apply (zenon_L468_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Haf | zenon_intro zenon_H187 ]. % 5.66/5.87 apply (zenon_L424_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H15e | zenon_intro zenon_H5f ]. % 5.66/5.87 apply (zenon_L485_); trivial. % 5.66/5.87 exact (zenon_H58 zenon_H5f). % 5.66/5.87 (* end of lemma zenon_L486_ *) % 5.66/5.87 assert (zenon_L487_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H3b zenon_H185 zenon_Hee zenon_H2c zenon_H1f2 zenon_Hd3 zenon_H9d zenon_H58. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.66/5.87 apply (zenon_L486_); trivial. % 5.66/5.87 (* end of lemma zenon_L487_ *) % 5.66/5.87 assert (zenon_L488_ : (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((op (e0) (e2)) = (e2)) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e2)) -> (~((op (e2) (e2)) = (e1))) -> ((op (e0) (e0)) = (e3)) -> ((op (e2) (e2)) = (e0)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H163 zenon_Hb0 zenon_H97 zenon_H73 zenon_H77 zenon_Hba zenon_H4f. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H149 | zenon_intro zenon_H164 ]. % 5.66/5.87 apply (zenon_L156_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H46 | zenon_intro zenon_H165 ]. % 5.66/5.87 apply (zenon_L49_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 5.66/5.87 exact (zenon_H77 zenon_H47). % 5.66/5.87 apply (zenon_L158_); trivial. % 5.66/5.87 (* end of lemma zenon_L488_ *) % 5.66/5.87 assert (zenon_L489_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((op (e2) (e0)) = (e2)) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H1cb zenon_H150 zenon_H2c zenon_H118 zenon_Hbe zenon_H97 zenon_H9d zenon_Hca. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.66/5.87 exact (zenon_H150 zenon_H152). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.66/5.87 apply (zenon_L88_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.66/5.87 apply (zenon_L338_); trivial. % 5.66/5.87 apply (zenon_L339_); trivial. % 5.66/5.87 (* end of lemma zenon_L489_ *) % 5.66/5.87 assert (zenon_L490_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H1d1 zenon_H195 zenon_H174 zenon_H179 zenon_H16e zenon_H169 zenon_H11f zenon_H12a zenon_H129 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf3 zenon_Hed zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hce zenon_Haa zenon_Ha7 zenon_H9f zenon_Hd9 zenon_H117 zenon_H9a zenon_H8f zenon_H72 zenon_H57 zenon_Hfd zenon_H100 zenon_H11e zenon_H185 zenon_H189 zenon_H20 zenon_H2c zenon_Hbe zenon_H63 zenon_H122 zenon_H13f zenon_H4a zenon_H45 zenon_H14b zenon_H3d zenon_H17d zenon_H118 zenon_H11a zenon_H188 zenon_H14f zenon_Hb4 zenon_H55 zenon_H105 zenon_H163 zenon_H9d zenon_H6d zenon_H26 zenon_H86 zenon_H171 zenon_H97 zenon_H1bf zenon_Hee zenon_H8e zenon_H25 zenon_Hb7 zenon_H150 zenon_Hf6 zenon_Hf0 zenon_H146 zenon_Hde zenon_H1f2 zenon_H198 zenon_H1a0 zenon_H1a5 zenon_H1cb. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.87 apply (zenon_L16_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.87 apply (zenon_L87_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.87 apply (zenon_L482_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.87 apply (zenon_L483_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.87 apply (zenon_L89_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.87 apply (zenon_L90_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.87 apply (zenon_L92_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.87 apply (zenon_L421_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.66/5.87 apply (zenon_L463_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.87 apply (zenon_L93_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.87 apply (zenon_L51_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.87 apply (zenon_L329_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.87 apply (zenon_L484_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.87 apply (zenon_L94_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.87 apply (zenon_L432_); trivial. % 5.66/5.87 apply (zenon_L284_); trivial. % 5.66/5.87 apply (zenon_L236_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.87 apply (zenon_L16_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.87 apply (zenon_L87_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.87 apply (zenon_L482_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.87 apply (zenon_L487_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.87 apply (zenon_L89_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.87 apply (zenon_L90_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.87 apply (zenon_L92_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.87 apply (zenon_L421_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.66/5.87 exact (zenon_H20 zenon_H1f). % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.87 exact (zenon_H150 zenon_H152). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.66/5.87 apply (zenon_L18_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.66/5.87 exact (zenon_H25 zenon_H2e). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H33 | zenon_intro zenon_H92 ]. % 5.66/5.87 apply (zenon_L176_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H74 | zenon_intro zenon_H93 ]. % 5.66/5.87 apply (zenon_L21_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H4f | zenon_intro zenon_H78 ]. % 5.66/5.87 apply (zenon_L488_); trivial. % 5.66/5.87 apply (zenon_L266_); trivial. % 5.66/5.87 apply (zenon_L462_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.87 apply (zenon_L102_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.87 apply (zenon_L270_); trivial. % 5.66/5.87 apply (zenon_L271_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.87 apply (zenon_L156_); trivial. % 5.66/5.87 apply (zenon_L161_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.66/5.87 apply (zenon_L320_); trivial. % 5.66/5.87 apply (zenon_L486_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.87 apply (zenon_L83_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.87 apply (zenon_L51_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.87 apply (zenon_L329_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.87 apply (zenon_L279_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.87 apply (zenon_L281_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.87 apply (zenon_L432_); trivial. % 5.66/5.87 apply (zenon_L284_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.87 apply (zenon_L16_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.87 apply (zenon_L87_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.87 apply (zenon_L482_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.87 apply (zenon_L483_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.87 apply (zenon_L89_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.87 apply (zenon_L90_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.87 apply (zenon_L92_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.87 apply (zenon_L295_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.66/5.87 apply (zenon_L477_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.87 apply (zenon_L93_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.87 apply (zenon_L51_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.87 apply (zenon_L329_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.87 apply (zenon_L299_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.87 apply (zenon_L94_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.87 apply (zenon_L303_); trivial. % 5.66/5.87 apply (zenon_L284_); trivial. % 5.66/5.87 apply (zenon_L42_); trivial. % 5.66/5.87 apply (zenon_L280_); trivial. % 5.66/5.87 apply (zenon_L489_); trivial. % 5.66/5.87 apply (zenon_L84_); trivial. % 5.66/5.87 apply (zenon_L85_); trivial. % 5.66/5.87 apply (zenon_L82_); trivial. % 5.66/5.87 (* end of lemma zenon_L490_ *) % 5.66/5.87 assert (zenon_L491_ : ((op (e3) (e0)) = (e0)) -> ((op (e3) (e0)) = (e2)) -> (~((e0) = (e2))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H39 zenon_H1c5 zenon_H63. % 5.66/5.87 elim (classic ((e2) = (e2))); [ zenon_intro zenon_H69 | zenon_intro zenon_H62 ]. % 5.66/5.87 cut (((e2) = (e2)) = ((e0) = (e2))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H63. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H69. % 5.66/5.87 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.87 cut (((e2) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 5.66/5.87 congruence. % 5.66/5.87 cut (((op (e3) (e0)) = (e0)) = ((e2) = (e0))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H6a. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H39. % 5.66/5.87 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.87 cut (((op (e3) (e0)) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 5.66/5.87 congruence. % 5.66/5.87 exact (zenon_H1c6 zenon_H1c5). % 5.66/5.87 apply zenon_H67. apply refl_equal. % 5.66/5.87 apply zenon_H62. apply refl_equal. % 5.66/5.87 apply zenon_H62. apply refl_equal. % 5.66/5.87 (* end of lemma zenon_L491_ *) % 5.66/5.87 assert (zenon_L492_ : (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e2)) -> ((op (e3) (e1)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H126 zenon_H1c5 zenon_Ha6 zenon_H6d zenon_Hc7 zenon_H63 zenon_Hf7. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H39 | zenon_intro zenon_H127 ]. % 5.66/5.87 apply (zenon_L491_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H124 | zenon_intro zenon_H128 ]. % 5.66/5.87 apply (zenon_L287_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_H78 | zenon_intro zenon_H5b ]. % 5.66/5.87 apply (zenon_L330_); trivial. % 5.66/5.87 exact (zenon_Hf7 zenon_H5b). % 5.66/5.87 (* end of lemma zenon_L492_ *) % 5.66/5.87 assert (zenon_L493_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H18e zenon_H6d zenon_H108 zenon_Ha3 zenon_Hee zenon_H4b zenon_H63 zenon_H64. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H18f ]. % 5.66/5.87 apply (zenon_L100_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H12f | zenon_intro zenon_H190 ]. % 5.66/5.87 apply (zenon_L122_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H4f | zenon_intro zenon_H65 ]. % 5.66/5.87 exact (zenon_H4b zenon_H4f). % 5.66/5.87 apply (zenon_L15_); trivial. % 5.66/5.87 (* end of lemma zenon_L493_ *) % 5.66/5.87 assert (zenon_L494_ : (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e3)) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e2))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H146 zenon_H9d zenon_H63 zenon_H4b zenon_Hee zenon_H108 zenon_H6d zenon_H18e zenon_H77 zenon_H97 zenon_H64. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H12b | zenon_intro zenon_H147 ]. % 5.66/5.87 apply (zenon_L409_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H148 ]. % 5.66/5.87 apply (zenon_L493_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H47 | zenon_intro zenon_H144 ]. % 5.66/5.87 exact (zenon_H77 zenon_H47). % 5.66/5.87 apply (zenon_L129_); trivial. % 5.66/5.87 (* end of lemma zenon_L494_ *) % 5.66/5.87 assert (zenon_L495_ : ((op (e3) (e1)) = (e3)) -> ((op (e2) (e1)) = (e3)) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> False). % 5.66/5.87 do 0 intro. intros zenon_Ha6 zenon_Ha4 zenon_H202. % 5.66/5.87 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1ec | zenon_intro zenon_H1a1 ]. % 5.66/5.87 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e2) (e1)) = (op (e3) (e1)))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H202. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H1ec. % 5.66/5.87 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 5.66/5.87 cut (((op (e3) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 5.66/5.87 congruence. % 5.66/5.87 cut (((op (e3) (e1)) = (e3)) = ((op (e3) (e1)) = (op (e2) (e1)))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H203. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_Ha6. % 5.66/5.87 cut (((e3) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 5.66/5.87 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 5.66/5.87 congruence. % 5.66/5.87 apply zenon_H1a1. apply refl_equal. % 5.66/5.87 apply zenon_H1af. apply sym_equal. exact zenon_Ha4. % 5.66/5.87 apply zenon_H1a1. apply refl_equal. % 5.66/5.87 apply zenon_H1a1. apply refl_equal. % 5.66/5.87 (* end of lemma zenon_L495_ *) % 5.66/5.87 assert (zenon_L496_ : (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e2))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e2)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> ((op (e3) (e0)) = (e0)) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e3)) = (e2)) -> (~((e2) = (e3))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H10d zenon_H77 zenon_H18e zenon_H6d zenon_H4b zenon_H63 zenon_H146 zenon_H202 zenon_H74 zenon_H97 zenon_Hc7 zenon_H9d zenon_Ha6 zenon_H39 zenon_Hee zenon_H185 zenon_H64 zenon_H86. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H108 | zenon_intro zenon_H10e ]. % 5.66/5.87 apply (zenon_L494_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H10f ]. % 5.66/5.87 apply (zenon_L495_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H51 | zenon_intro zenon_Hcd ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H182 | zenon_intro zenon_H186 ]. % 5.66/5.87 apply (zenon_L468_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Haf | zenon_intro zenon_H187 ]. % 5.66/5.87 apply (zenon_L294_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H15e | zenon_intro zenon_H5f ]. % 5.66/5.87 apply (zenon_L363_); trivial. % 5.66/5.87 apply (zenon_notand_s _ _ ax26); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H204 ]. % 5.66/5.87 apply zenon_H1d8. apply sym_equal. exact zenon_H51. % 5.66/5.87 apply (zenon_notand_s _ _ zenon_H204); [ zenon_intro zenon_H205 | zenon_intro zenon_H7a ]. % 5.66/5.87 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.66/5.87 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((e1) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H205. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H7c. % 5.66/5.87 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.66/5.87 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 5.66/5.87 congruence. % 5.66/5.87 cut (((op (e3) (e3)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H206. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H5f. % 5.66/5.87 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.87 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 5.66/5.87 congruence. % 5.66/5.87 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.66/5.87 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H1db. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H7c. % 5.66/5.87 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.66/5.87 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 5.66/5.87 congruence. % 5.66/5.87 apply (zenon_L361_); trivial. % 5.66/5.87 apply zenon_H7d. apply refl_equal. % 5.66/5.87 apply zenon_H7d. apply refl_equal. % 5.66/5.87 apply zenon_H94. apply refl_equal. % 5.66/5.87 apply zenon_H7d. apply refl_equal. % 5.66/5.87 apply zenon_H7d. apply refl_equal. % 5.66/5.87 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H80 | zenon_intro zenon_H81 ]. % 5.66/5.87 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2))) = ((e0) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H7a. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H80. % 5.66/5.87 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 5.66/5.87 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 5.66/5.87 congruence. % 5.66/5.87 cut (((op (e1) (e2)) = (e0)) = ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (e0))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H82. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H74. % 5.66/5.87 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.87 cut (((op (e1) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 5.66/5.87 congruence. % 5.66/5.87 elim (classic ((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [ zenon_intro zenon_H80 | zenon_intro zenon_H81 ]. % 5.66/5.87 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2))) = ((op (e1) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H207. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H80. % 5.66/5.87 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (op (op (e2) (e2)) (op (e2) (e2))) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 5.66/5.87 cut (((op (op (op (e2) (e2)) (op (e2) (e2))) (e2)) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 5.66/5.87 congruence. % 5.66/5.87 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.87 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 5.66/5.87 congruence. % 5.66/5.87 cut (((op (e3) (e3)) = (e1)) = ((op (op (e2) (e2)) (op (e2) (e2))) = (e1))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H206. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H5f. % 5.66/5.87 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.87 cut (((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 5.66/5.87 congruence. % 5.66/5.87 elim (classic ((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [ zenon_intro zenon_H7c | zenon_intro zenon_H7d ]. % 5.66/5.87 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2)))) = ((op (e3) (e3)) = (op (op (e2) (e2)) (op (e2) (e2))))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H1db. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H7c. % 5.66/5.87 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (op (e2) (e2)) (op (e2) (e2))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 5.66/5.87 cut (((op (op (e2) (e2)) (op (e2) (e2))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 5.66/5.87 congruence. % 5.66/5.87 apply (zenon_L361_); trivial. % 5.66/5.87 apply zenon_H7d. apply refl_equal. % 5.66/5.87 apply zenon_H7d. apply refl_equal. % 5.66/5.87 apply zenon_H94. apply refl_equal. % 5.66/5.87 apply zenon_H62. apply refl_equal. % 5.66/5.87 apply zenon_H81. apply refl_equal. % 5.66/5.87 apply zenon_H81. apply refl_equal. % 5.66/5.87 apply zenon_H67. apply refl_equal. % 5.66/5.87 apply zenon_H81. apply refl_equal. % 5.66/5.87 apply zenon_H81. apply refl_equal. % 5.66/5.87 apply (zenon_L282_); trivial. % 5.66/5.87 (* end of lemma zenon_L496_ *) % 5.66/5.87 assert (zenon_L497_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H17d zenon_H122 zenon_H13f zenon_H86 zenon_H64 zenon_H185 zenon_Hee zenon_H39 zenon_Ha6 zenon_H9d zenon_Hc7 zenon_H97 zenon_H202 zenon_H146 zenon_H63 zenon_H4b zenon_H6d zenon_H18e zenon_H77 zenon_H10d zenon_H14b zenon_H3d. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.87 apply (zenon_L112_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.87 exact (zenon_H13f zenon_H28). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.87 apply (zenon_L496_); trivial. % 5.66/5.87 apply (zenon_L180_); trivial. % 5.66/5.87 (* end of lemma zenon_L497_ *) % 5.66/5.87 assert (zenon_L498_ : (~((op (e3) (e3)) = (e0))) -> (((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) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> False). % 5.66/5.87 do 0 intro. intros zenon_Hf7 zenon_H126 zenon_H1d1 zenon_H195 zenon_H174 zenon_H179 zenon_H16e zenon_H169 zenon_H11f zenon_H12a zenon_H129 zenon_H123 zenon_H143 zenon_H140 zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H110 zenon_H113 zenon_H116 zenon_Hf3 zenon_Hed zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hce zenon_Haa zenon_Ha7 zenon_H9f zenon_Hd9 zenon_H117 zenon_H9a zenon_H8f zenon_H72 zenon_H57 zenon_Hfd zenon_H100 zenon_H11e zenon_H189 zenon_H20 zenon_H4a zenon_H45 zenon_H118 zenon_H188 zenon_H14f zenon_Hb4 zenon_H55 zenon_H105 zenon_H163 zenon_H26 zenon_H171 zenon_H1bf zenon_H8e zenon_H25 zenon_Hb7 zenon_H150 zenon_Hf6 zenon_Hf0 zenon_Hde zenon_H1f2 zenon_H198 zenon_H1a0 zenon_H1a5 zenon_H1cb zenon_H16a zenon_H1c7 zenon_H11a zenon_H2c zenon_H17d zenon_H122 zenon_H13f zenon_H86 zenon_H64 zenon_H185 zenon_Hee zenon_Ha6 zenon_H9d zenon_Hc7 zenon_H97 zenon_H202 zenon_H146 zenon_H63 zenon_H4b zenon_H6d zenon_H18e zenon_H77 zenon_H10d zenon_H14b zenon_H3d. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.66/5.87 exact (zenon_H20 zenon_H1f). % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.66/5.87 exact (zenon_H16a zenon_H16c). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.66/5.87 apply (zenon_L18_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.66/5.87 apply (zenon_L490_); trivial. % 5.66/5.87 apply (zenon_L492_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.66/5.87 apply (zenon_L146_); trivial. % 5.66/5.87 apply (zenon_L497_); trivial. % 5.66/5.87 (* end of lemma zenon_L498_ *) % 5.66/5.87 assert (zenon_L499_ : (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((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) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> ((op (e3) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H59 zenon_Hb8 zenon_H1ff zenon_Hf7 zenon_H126 zenon_H1d1 zenon_H195 zenon_H174 zenon_H179 zenon_H16e zenon_H169 zenon_H11f zenon_H12a zenon_H129 zenon_H123 zenon_H143 zenon_H140 zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H110 zenon_H113 zenon_H116 zenon_Hf3 zenon_Hed zenon_Hf8 zenon_Hdd zenon_Hdc zenon_Hce zenon_Haa zenon_Ha7 zenon_H9f zenon_Hd9 zenon_H117 zenon_H9a zenon_H8f zenon_H72 zenon_H57 zenon_Hfd zenon_H100 zenon_H11e zenon_H189 zenon_H20 zenon_H4a zenon_H45 zenon_H118 zenon_H188 zenon_H14f zenon_Hb4 zenon_H55 zenon_H105 zenon_H163 zenon_H26 zenon_H171 zenon_H1bf zenon_H8e zenon_H25 zenon_Hb7 zenon_H150 zenon_Hf6 zenon_Hf0 zenon_Hde zenon_H1f2 zenon_H198 zenon_H1a0 zenon_H1a5 zenon_H1cb zenon_H16a zenon_H1c7 zenon_H11a zenon_H2c zenon_H17d zenon_H122 zenon_H13f zenon_H86 zenon_H64 zenon_H185 zenon_Hee zenon_Ha6 zenon_H9d zenon_Hc7 zenon_H97 zenon_H202 zenon_H146 zenon_H63 zenon_H4b zenon_H6d zenon_H18e zenon_H77 zenon_H10d zenon_H14b. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.66/5.87 exact (zenon_H20 zenon_H1f). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.66/5.87 apply (zenon_L358_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.66/5.87 apply (zenon_L481_); trivial. % 5.66/5.87 apply (zenon_L498_); trivial. % 5.66/5.87 (* end of lemma zenon_L499_ *) % 5.66/5.87 assert (zenon_L500_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H1cb zenon_H150 zenon_H2c zenon_H118 zenon_Hee zenon_Hd6 zenon_H9d zenon_Hca. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.66/5.87 exact (zenon_H150 zenon_H152). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.66/5.87 apply (zenon_L88_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.66/5.87 apply (zenon_L121_); trivial. % 5.66/5.87 apply (zenon_L339_); trivial. % 5.66/5.87 (* end of lemma zenon_L500_ *) % 5.66/5.87 assert (zenon_L501_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H36 zenon_H1cb zenon_H150 zenon_H2c zenon_H118 zenon_Hee zenon_H9d zenon_Hca. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_Hd6. zenon_intro zenon_H4c. % 5.66/5.87 apply (zenon_L500_); trivial. % 5.66/5.87 (* end of lemma zenon_L501_ *) % 5.66/5.87 assert (zenon_L502_ : (((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e1) = (e2))) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.87 do 0 intro. intros zenon_Hbc zenon_H1cb zenon_H150 zenon_H2c zenon_H118 zenon_H97 zenon_H9d zenon_Hca. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.66/5.87 apply (zenon_L489_); trivial. % 5.66/5.87 (* end of lemma zenon_L502_ *) % 5.66/5.87 assert (zenon_L503_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e3) (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 (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((e1) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H171 zenon_H3e zenon_H59 zenon_Hb4 zenon_Hf7 zenon_H55 zenon_H2c zenon_H188 zenon_H64 zenon_H97 zenon_H58. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H14a | zenon_intro zenon_H172 ]. % 5.66/5.87 apply (zenon_L292_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_H173 ]. % 5.66/5.87 apply (zenon_L217_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H144 | zenon_intro zenon_H5f ]. % 5.66/5.87 apply (zenon_L129_); trivial. % 5.66/5.87 exact (zenon_H58 zenon_H5f). % 5.66/5.87 (* end of lemma zenon_L503_ *) % 5.66/5.87 assert (zenon_L504_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e0)) = (e0)) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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 (e3) (e3)) = (e3))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H14f zenon_H150 zenon_H143 zenon_H1d1 zenon_H25 zenon_H140 zenon_H3d zenon_H14b zenon_H1e9 zenon_H4c zenon_H17d zenon_H122 zenon_H13f zenon_H86 zenon_H64 zenon_H185 zenon_Hee zenon_H39 zenon_Ha6 zenon_H9d zenon_H97 zenon_H202 zenon_H146 zenon_H63 zenon_H4b zenon_H6d zenon_H18e zenon_H77 zenon_H10d zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.87 exact (zenon_H150 zenon_H152). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.87 apply (zenon_L352_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.87 apply (zenon_L112_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.87 exact (zenon_H13f zenon_H28). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H1ea ]. % 5.66/5.87 apply (zenon_L156_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_H73 | zenon_intro zenon_H1eb ]. % 5.66/5.87 apply (zenon_L21_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1eb); [ zenon_intro zenon_H52 | zenon_intro zenon_Hc7 ]. % 5.66/5.87 exact (zenon_H4c zenon_H52). % 5.66/5.87 apply (zenon_L497_); trivial. % 5.66/5.87 apply (zenon_L180_); trivial. % 5.66/5.87 apply (zenon_L292_); trivial. % 5.66/5.87 (* end of lemma zenon_L504_ *) % 5.66/5.87 assert (zenon_L505_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> False). % 5.66/5.87 do 0 intro. intros zenon_Hde zenon_H11a zenon_H188 zenon_Hf0 zenon_H129 zenon_H58 zenon_H97 zenon_H1f2 zenon_H185 zenon_H6d zenon_H1cb zenon_H150 zenon_H2c zenon_H118 zenon_Hee zenon_H9d zenon_H105 zenon_H63 zenon_H25 zenon_H14b zenon_H26 zenon_H8e zenon_H1ff zenon_Hf6 zenon_Hca zenon_H143 zenon_H86 zenon_H64. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.87 apply (zenon_L16_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.87 apply (zenon_L87_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.87 apply (zenon_L501_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.87 apply (zenon_L305_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.87 apply (zenon_L89_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.87 apply (zenon_L90_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.87 apply (zenon_L92_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.87 apply (zenon_L421_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.87 apply (zenon_L173_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.87 apply (zenon_L138_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.87 apply (zenon_L51_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.87 apply (zenon_L426_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.66/5.87 exact (zenon_H20 zenon_H1f). % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.66/5.87 apply (zenon_L479_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.66/5.87 apply (zenon_L500_); trivial. % 5.66/5.87 apply (zenon_L304_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.87 apply (zenon_L307_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.87 apply (zenon_L283_); trivial. % 5.66/5.87 apply (zenon_L284_); trivial. % 5.66/5.87 (* end of lemma zenon_L505_ *) % 5.66/5.87 assert (zenon_L506_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (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 (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e3)) = (e2)) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H179 zenon_Hde zenon_H143 zenon_Hf6 zenon_H63 zenon_H25 zenon_H8e zenon_H14b zenon_H86 zenon_H26 zenon_H1ff zenon_H105 zenon_H185 zenon_H97 zenon_H1f2 zenon_H129 zenon_Hf0 zenon_H64 zenon_H188 zenon_H11a zenon_H6d zenon_H1cb zenon_Hca zenon_H9d zenon_Hee zenon_H118 zenon_H150 zenon_H2c. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.87 apply (zenon_L505_); trivial. % 5.66/5.87 apply (zenon_L298_); trivial. % 5.66/5.87 (* end of lemma zenon_L506_ *) % 5.66/5.87 assert (zenon_L507_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e3) (e1)) = (e1)) -> (~((e1) = (e2))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H1d1 zenon_H63 zenon_H22 zenon_H25 zenon_H52 zenon_Hd9 zenon_Haf zenon_H97. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H15a | zenon_intro zenon_H1d2 ]. % 5.66/5.87 apply (zenon_L357_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H2e | zenon_intro zenon_H1d3 ]. % 5.66/5.87 exact (zenon_H25 zenon_H2e). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1cf ]. % 5.66/5.87 apply (zenon_L60_); trivial. % 5.66/5.87 apply (zenon_L368_); trivial. % 5.66/5.87 (* end of lemma zenon_L507_ *) % 5.66/5.87 assert (zenon_L508_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> False). % 5.66/5.87 do 0 intro. intros zenon_Had zenon_H1d1 zenon_H63 zenon_H22 zenon_H25 zenon_H52 zenon_Hd9 zenon_H97. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.66/5.87 apply (zenon_L507_); trivial. % 5.66/5.87 (* end of lemma zenon_L508_ *) % 5.66/5.87 assert (zenon_L509_ : (((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 (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H169 zenon_H16a zenon_H63 zenon_H22 zenon_H11f zenon_H52 zenon_H86 zenon_Hb3. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.87 exact (zenon_H16a zenon_H16c). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.87 apply (zenon_L357_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.87 apply (zenon_L187_); trivial. % 5.66/5.87 apply (zenon_L401_); trivial. % 5.66/5.87 (* end of lemma zenon_L509_ *) % 5.66/5.87 assert (zenon_L510_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (((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 (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> False). % 5.66/5.87 do 0 intro. intros zenon_Hc8 zenon_H169 zenon_H16a zenon_H63 zenon_H22 zenon_H11f zenon_H52 zenon_H86. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.66/5.87 apply (zenon_L509_); trivial. % 5.66/5.87 (* end of lemma zenon_L510_ *) % 5.66/5.87 assert (zenon_L511_ : (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H1d1 zenon_H63 zenon_H22 zenon_H25 zenon_H52 zenon_Hd9 zenon_H86 zenon_Ha6. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1d1); [ zenon_intro zenon_H15a | zenon_intro zenon_H1d2 ]. % 5.66/5.87 apply (zenon_L357_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1d2); [ zenon_intro zenon_H2e | zenon_intro zenon_H1d3 ]. % 5.66/5.87 exact (zenon_H25 zenon_H2e). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1d3); [ zenon_intro zenon_Hc2 | zenon_intro zenon_H1cf ]. % 5.66/5.87 apply (zenon_L60_); trivial. % 5.66/5.87 apply (zenon_L350_); trivial. % 5.66/5.87 (* end of lemma zenon_L511_ *) % 5.66/5.87 assert (zenon_L512_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> False). % 5.66/5.87 do 0 intro. intros zenon_Hcb zenon_H1d1 zenon_H63 zenon_H22 zenon_H25 zenon_H52 zenon_Hd9 zenon_H86. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.87 apply (zenon_L511_); trivial. % 5.66/5.87 (* end of lemma zenon_L512_ *) % 5.66/5.87 assert (zenon_L513_ : ((op (e2) (e3)) = (e0)) -> ((op (e1) (e1)) = (e2)) -> ((op (e3) (e3)) = (e1)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H65 zenon_H2e zenon_H5f. % 5.66/5.87 apply (zenon_notand_s _ _ ax14); [ zenon_intro zenon_H1aa | zenon_intro zenon_H209 ]. % 5.66/5.87 apply zenon_H1aa. apply sym_equal. exact zenon_H5f. % 5.66/5.87 apply (zenon_notand_s _ _ zenon_H209); [ zenon_intro zenon_H20b | zenon_intro zenon_H20a ]. % 5.66/5.87 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.87 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e2) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H20b. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H1b6. % 5.66/5.87 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.87 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20c]. % 5.66/5.87 congruence. % 5.66/5.87 cut (((op (e1) (e1)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H20c. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H2e. % 5.66/5.87 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.87 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 5.66/5.87 congruence. % 5.66/5.87 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.87 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H1f6. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H1b6. % 5.66/5.87 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.87 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 5.66/5.87 congruence. % 5.66/5.87 apply (zenon_L437_); trivial. % 5.66/5.87 apply zenon_H1b7. apply refl_equal. % 5.66/5.87 apply zenon_H1b7. apply refl_equal. % 5.66/5.87 apply zenon_H62. apply refl_equal. % 5.66/5.87 apply zenon_H1b7. apply refl_equal. % 5.66/5.87 apply zenon_H1b7. apply refl_equal. % 5.66/5.87 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.66/5.87 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H20a. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H1ba. % 5.66/5.87 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.66/5.87 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H20d]. % 5.66/5.87 congruence. % 5.66/5.87 cut (((op (e2) (e3)) = (e0)) = ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e0))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H20d. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H65. % 5.66/5.87 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.66/5.87 cut (((op (e2) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 5.66/5.87 congruence. % 5.66/5.87 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.66/5.87 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((op (e2) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H20e. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H1ba. % 5.66/5.87 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.66/5.87 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 5.66/5.87 congruence. % 5.66/5.87 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.87 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20c]. % 5.66/5.87 congruence. % 5.66/5.87 cut (((op (e1) (e1)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H20c. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H2e. % 5.66/5.87 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.87 cut (((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 5.66/5.87 congruence. % 5.66/5.87 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.87 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e1) (e1)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.87 intro zenon_D_pnotp. % 5.66/5.87 apply zenon_H1f6. % 5.66/5.87 rewrite <- zenon_D_pnotp. % 5.66/5.87 exact zenon_H1b6. % 5.66/5.87 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.87 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 5.66/5.87 congruence. % 5.66/5.87 apply (zenon_L437_); trivial. % 5.66/5.87 apply zenon_H1b7. apply refl_equal. % 5.66/5.87 apply zenon_H1b7. apply refl_equal. % 5.66/5.87 apply zenon_H62. apply refl_equal. % 5.66/5.87 apply zenon_H6f. apply refl_equal. % 5.66/5.87 apply zenon_H1bb. apply refl_equal. % 5.66/5.87 apply zenon_H1bb. apply refl_equal. % 5.66/5.87 apply zenon_H67. apply refl_equal. % 5.66/5.87 apply zenon_H1bb. apply refl_equal. % 5.66/5.87 apply zenon_H1bb. apply refl_equal. % 5.66/5.87 (* end of lemma zenon_L513_ *) % 5.66/5.87 assert (zenon_L514_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e1) (e1)) = (e2)) -> ((op (e2) (e3)) = (e0)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H55 zenon_Hf7 zenon_H2e zenon_H65 zenon_H59 zenon_H3e. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 5.66/5.87 exact (zenon_Hf7 zenon_H5b). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 5.66/5.87 apply (zenon_L513_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 5.66/5.87 exact (zenon_H59 zenon_H61). % 5.66/5.87 exact (zenon_H3e zenon_H60). % 5.66/5.87 (* end of lemma zenon_L514_ *) % 5.66/5.87 assert (zenon_L515_ : (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> ((op (e1) (e3)) = (e2)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H8e zenon_H6d zenon_H31 zenon_H26 zenon_H9d zenon_H46 zenon_H86 zenon_H96. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.87 apply (zenon_L19_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.87 exact (zenon_H26 zenon_H2d). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.87 apply (zenon_L35_); trivial. % 5.66/5.87 apply (zenon_L398_); trivial. % 5.66/5.87 (* end of lemma zenon_L515_ *) % 5.66/5.87 assert (zenon_L516_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e0) (e3)) = (e2)) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e0) = (e3))) -> ((op (e1) (e0)) = (e0)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> ((op (e1) (e2)) = (e1)) -> (~((e2) = (e3))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H105 zenon_Hf7 zenon_H55 zenon_H59 zenon_H3e zenon_H167 zenon_H63 zenon_Hf8 zenon_H97 zenon_H8e zenon_H6d zenon_H31 zenon_H26 zenon_H9d zenon_H46 zenon_H86. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.66/5.87 apply (zenon_L18_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.87 apply (zenon_L19_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.87 exact (zenon_H26 zenon_H2d). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.87 apply (zenon_L35_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H3d | zenon_intro zenon_Hfb ]. % 5.66/5.87 apply (zenon_L163_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H56 | zenon_intro zenon_Hfc ]. % 5.66/5.87 apply (zenon_L301_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H65 | zenon_intro zenon_H5b ]. % 5.66/5.87 apply (zenon_L514_); trivial. % 5.66/5.87 exact (zenon_Hf7 zenon_H5b). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.66/5.87 apply (zenon_L49_); trivial. % 5.66/5.87 apply (zenon_L515_); trivial. % 5.66/5.87 (* end of lemma zenon_L516_ *) % 5.66/5.87 assert (zenon_L517_ : (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e3)) -> ((op (e2) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e0))) -> ((op (e1) (e1)) = (e2)) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H18e zenon_H6d zenon_H108 zenon_Ha3 zenon_Hee zenon_H4b zenon_H55 zenon_Hf7 zenon_H2e zenon_H59 zenon_H3e. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H18f ]. % 5.66/5.87 apply (zenon_L100_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H12f | zenon_intro zenon_H190 ]. % 5.66/5.87 apply (zenon_L122_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H4f | zenon_intro zenon_H65 ]. % 5.66/5.87 exact (zenon_H4b zenon_H4f). % 5.66/5.87 apply (zenon_L514_); trivial. % 5.66/5.87 (* end of lemma zenon_L517_ *) % 5.66/5.87 assert (zenon_L518_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H1c7 zenon_H16a zenon_H63 zenon_H31 zenon_H52 zenon_H113 zenon_H86 zenon_Hca. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.66/5.87 exact (zenon_H16a zenon_H16c). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.66/5.87 apply (zenon_L18_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.66/5.87 apply (zenon_L85_); trivial. % 5.66/5.87 apply (zenon_L334_); trivial. % 5.66/5.87 (* end of lemma zenon_L518_ *) % 5.66/5.87 assert (zenon_L519_ : (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e1) (e0)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H10a zenon_Hb8 zenon_Ha6 zenon_H9d zenon_H105 zenon_H3e zenon_H59 zenon_Hf7 zenon_H55 zenon_H4b zenon_Hee zenon_H6d zenon_H18e zenon_H97 zenon_H46 zenon_H89 zenon_H24 zenon_H22 zenon_H1c2 zenon_H1c7 zenon_H16a zenon_H63 zenon_H31 zenon_H52 zenon_H113 zenon_H86. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.87 exact (zenon_Hb8 zenon_Hba). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.87 apply (zenon_L19_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H42 | zenon_intro zenon_H1c3 ]. % 5.66/5.87 apply (zenon_L154_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c4 ]. % 5.66/5.87 exact (zenon_H24 zenon_H2c). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Haf ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.66/5.87 apply (zenon_L18_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.66/5.87 apply (zenon_L517_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.66/5.87 apply (zenon_L49_); trivial. % 5.66/5.87 apply (zenon_L398_); trivial. % 5.66/5.87 apply (zenon_L294_); trivial. % 5.66/5.87 apply (zenon_L518_); trivial. % 5.66/5.87 (* end of lemma zenon_L519_ *) % 5.66/5.87 assert (zenon_L520_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H2f zenon_H1c7 zenon_H16a zenon_H63 zenon_H52 zenon_H113 zenon_H86 zenon_Hca. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H31. zenon_intro zenon_H24. % 5.66/5.87 apply (zenon_L518_); trivial. % 5.66/5.87 (* end of lemma zenon_L520_ *) % 5.66/5.87 assert (zenon_L521_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.66/5.87 do 0 intro. intros zenon_Hde zenon_H113 zenon_H1c7 zenon_H72 zenon_H6d zenon_H9f zenon_H59 zenon_H1e2 zenon_H1e3 zenon_H97 zenon_H46 zenon_H1ad zenon_H86 zenon_H11f zenon_H22 zenon_H63 zenon_H16a zenon_H169 zenon_Hca zenon_H143 zenon_H52. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.87 apply (zenon_L16_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.87 apply (zenon_L520_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.87 apply (zenon_L31_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.87 apply (zenon_L305_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.87 apply (zenon_L39_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.87 apply (zenon_L9_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.87 apply (zenon_L59_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.87 apply (zenon_L377_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.87 apply (zenon_L190_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.87 apply (zenon_L50_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.87 apply (zenon_L62_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.87 apply (zenon_L310_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.87 apply (zenon_L510_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.87 apply (zenon_L307_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.87 apply (zenon_L63_); trivial. % 5.66/5.87 apply (zenon_L284_); trivial. % 5.66/5.87 (* end of lemma zenon_L521_ *) % 5.66/5.87 assert (zenon_L522_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e1) (e2)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.66/5.87 do 0 intro. intros zenon_Hde zenon_H113 zenon_H1c7 zenon_H72 zenon_H6d zenon_H9f zenon_H59 zenon_H1e2 zenon_H1e3 zenon_H97 zenon_H46 zenon_H1ad zenon_H86 zenon_H11f zenon_H22 zenon_H63 zenon_H16a zenon_H169 zenon_Hca zenon_H143 zenon_H52. % 5.66/5.87 apply (zenon_L521_); trivial. % 5.66/5.87 (* end of lemma zenon_L522_ *) % 5.66/5.87 assert (zenon_L523_ : ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (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 (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H1a5 zenon_Hf3 zenon_Hde zenon_H143 zenon_H169 zenon_H1ad zenon_H11f zenon_H1e3 zenon_H1e2 zenon_H97 zenon_H9f zenon_H46 zenon_H6d zenon_H72 zenon_H22 zenon_H1c7 zenon_Hca zenon_H86 zenon_H52 zenon_H113 zenon_H63 zenon_H16a. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.87 apply (zenon_L522_); trivial. % 5.66/5.87 apply (zenon_L278_); trivial. % 5.66/5.87 (* end of lemma zenon_L523_ *) % 5.66/5.87 assert (zenon_L524_ : (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H17d zenon_H39 zenon_H122 zenon_H13f zenon_H46 zenon_Hee zenon_H6d zenon_H89. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.87 apply (zenon_L112_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.87 exact (zenon_H13f zenon_H28). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.87 apply (zenon_L300_); trivial. % 5.66/5.87 apply (zenon_L301_); trivial. % 5.66/5.87 (* end of lemma zenon_L524_ *) % 5.66/5.87 assert (zenon_L525_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (((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 (e3) (e3)) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e2))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((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)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e3))) -> ((op (e1) (e3)) = (e3)) -> False). % 5.66/5.87 do 0 intro. intros zenon_Hf6 zenon_H1c2 zenon_H18e zenon_H4b zenon_H55 zenon_Hf7 zenon_H59 zenon_H3e zenon_H105 zenon_H9d zenon_Ha6 zenon_H20 zenon_H16a zenon_H63 zenon_H113 zenon_H52 zenon_H86 zenon_H1c7 zenon_H22 zenon_H72 zenon_H9f zenon_H24 zenon_H97 zenon_H1e2 zenon_H1e3 zenon_H11f zenon_H1ad zenon_H169 zenon_H143 zenon_Hde zenon_Hf3 zenon_H1a5 zenon_Hb8 zenon_H10a zenon_H17d zenon_H122 zenon_H13f zenon_H46 zenon_Hee zenon_H6d zenon_H89. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.66/5.87 exact (zenon_H20 zenon_H1f). % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.66/5.87 apply (zenon_L519_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.66/5.87 exact (zenon_Hb8 zenon_Hba). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.66/5.87 apply (zenon_L19_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.66/5.87 exact (zenon_H13f zenon_H28). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.66/5.87 apply (zenon_L300_); trivial. % 5.66/5.87 apply (zenon_L301_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.66/5.87 apply (zenon_L100_); trivial. % 5.66/5.87 apply (zenon_L523_); trivial. % 5.66/5.87 apply (zenon_L524_); trivial. % 5.66/5.87 (* end of lemma zenon_L525_ *) % 5.66/5.87 assert (zenon_L526_ : (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((op (e0) (e2)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((e0) = (e1))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e3) (e2)) = (e3)) -> False). % 5.66/5.87 do 0 intro. intros zenon_H8f zenon_Hb1 zenon_H46 zenon_Hee zenon_H4b zenon_H6d zenon_Hd3. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H8f); [ zenon_intro zenon_H33 | zenon_intro zenon_H92 ]. % 5.66/5.87 apply (zenon_L103_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H74 | zenon_intro zenon_H93 ]. % 5.66/5.87 apply (zenon_L300_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H4f | zenon_intro zenon_H78 ]. % 5.66/5.87 exact (zenon_H4b zenon_H4f). % 5.66/5.87 apply (zenon_L266_); trivial. % 5.66/5.87 (* end of lemma zenon_L526_ *) % 5.66/5.87 assert (zenon_L527_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.66/5.87 do 0 intro. intros zenon_Hde zenon_Hed zenon_H118 zenon_H188 zenon_Hd9 zenon_H1ad zenon_H86 zenon_H11f zenon_H22 zenon_H63 zenon_H16a zenon_H169 zenon_H2c zenon_H52. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.87 apply (zenon_L16_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.87 apply (zenon_L87_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.87 apply (zenon_L58_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.87 apply (zenon_L449_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.87 apply (zenon_L89_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.87 apply (zenon_L90_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.87 apply (zenon_L59_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.87 apply (zenon_L421_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.87 apply (zenon_L190_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.87 apply (zenon_L61_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.87 apply (zenon_L62_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.87 apply (zenon_L310_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.87 apply (zenon_L510_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.87 apply (zenon_L94_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.87 apply (zenon_L63_); trivial. % 5.66/5.87 apply (zenon_L284_); trivial. % 5.66/5.87 (* end of lemma zenon_L527_ *) % 5.66/5.87 assert (zenon_L528_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((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)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H188 zenon_H118 zenon_H11e zenon_Hde zenon_H169 zenon_H86 zenon_H16a zenon_H1ad zenon_H11f zenon_H1d1 zenon_Hd9 zenon_Hdc zenon_H9a zenon_Hed zenon_H72 zenon_H105 zenon_H97 zenon_H52 zenon_H45 zenon_H63 zenon_H20 zenon_H114 zenon_H115 zenon_H10a zenon_H113 zenon_Hf6 zenon_Hf3 zenon_Hee zenon_Hf8 zenon_Hdd zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Hb8 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_H6d zenon_H8f zenon_H57 zenon_H8e zenon_H100 zenon_H195 zenon_H23 zenon_H22 zenon_H21 zenon_H55 zenon_H1c7 zenon_H18e zenon_H1c2 zenon_H1e2 zenon_H1e3 zenon_H143 zenon_H1a5 zenon_H13f zenon_H17d zenon_H122. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.66/5.87 apply (zenon_L2_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.87 apply (zenon_L16_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.87 apply (zenon_L76_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.87 apply (zenon_L31_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.87 apply (zenon_L449_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.87 apply (zenon_L34_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.87 apply (zenon_L9_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.87 apply (zenon_L208_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.87 apply (zenon_L508_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.87 apply (zenon_L190_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.87 apply (zenon_L61_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.87 apply (zenon_L62_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.87 apply (zenon_L310_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.87 apply (zenon_L510_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.87 apply (zenon_L512_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.87 apply (zenon_L63_); trivial. % 5.66/5.87 apply (zenon_L284_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.87 apply (zenon_L16_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.66/5.87 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H31. zenon_intro zenon_H24. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.87 exact (zenon_H16a zenon_H16c). % 5.66/5.87 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.87 apply (zenon_L357_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.87 apply (zenon_L187_); trivial. % 5.66/5.87 apply (zenon_L516_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.87 apply (zenon_L58_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.87 apply (zenon_L449_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.87 apply (zenon_L39_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.87 apply (zenon_L9_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.87 apply (zenon_L59_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.87 apply (zenon_L306_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.87 apply (zenon_L190_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.87 apply (zenon_L61_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.87 apply (zenon_L62_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.87 apply (zenon_L310_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.87 apply (zenon_L510_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.66/5.87 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.66/5.87 apply (zenon_L525_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.87 apply (zenon_L63_); trivial. % 5.66/5.87 apply (zenon_L284_); trivial. % 5.66/5.87 apply (zenon_L65_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.66/5.87 exact (zenon_Hb8 zenon_Hba). % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.66/5.87 apply (zenon_L40_); trivial. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.66/5.87 apply (zenon_L526_); trivial. % 5.66/5.87 apply (zenon_L509_); trivial. % 5.66/5.87 apply (zenon_L523_); trivial. % 5.66/5.87 apply (zenon_L85_); trivial. % 5.66/5.87 apply (zenon_L64_); trivial. % 5.66/5.87 apply (zenon_L527_); trivial. % 5.66/5.87 (* end of lemma zenon_L528_ *) % 5.66/5.87 assert (zenon_L529_ : ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e1))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e0)) = (e1)) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H114 zenon_H9f zenon_H21 zenon_H24 zenon_H22 zenon_H23 zenon_H9a zenon_H41 zenon_Hdd. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.66/5.87 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.66/5.87 apply (zenon_L2_); trivial. % 5.66/5.87 apply (zenon_L33_); trivial. % 5.66/5.87 apply (zenon_L38_); trivial. % 5.66/5.87 (* end of lemma zenon_L529_ *) % 5.66/5.87 assert (zenon_L530_ : ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> False). % 5.66/5.87 do 0 intro. intros zenon_H11e zenon_H118 zenon_Hdd zenon_H41 zenon_H9a zenon_H23 zenon_H22 zenon_H21 zenon_H9f zenon_H114. % 5.66/5.87 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.66/5.87 apply (zenon_L529_); trivial. % 5.66/5.87 apply (zenon_L88_); trivial. % 5.66/5.87 (* end of lemma zenon_L530_ *) % 5.66/5.87 assert (zenon_L531_ : (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e0) (e1)) = (e0)) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 5.66/5.88 do 0 intro. intros zenon_H122 zenon_H17d zenon_H1a5 zenon_H143 zenon_H1e3 zenon_H1e2 zenon_H1c2 zenon_H18e zenon_H1c7 zenon_H55 zenon_H21 zenon_H22 zenon_H23 zenon_H195 zenon_H100 zenon_H8e zenon_H57 zenon_H8f zenon_H6d zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hdd zenon_Hf8 zenon_Hee zenon_Hf3 zenon_Hf6 zenon_H113 zenon_H10a zenon_H115 zenon_H114 zenon_H20 zenon_H63 zenon_H45 zenon_H52 zenon_H97 zenon_H105 zenon_H72 zenon_Hed zenon_H9a zenon_Hdc zenon_Hd9 zenon_H1d1 zenon_H11f zenon_H1ad zenon_H86 zenon_H169 zenon_Hde zenon_H158 zenon_H11d zenon_H11e zenon_H189 zenon_H118 zenon_H188. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H189); [ zenon_intro zenon_H16a | zenon_intro zenon_H33 ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H3d ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.66/5.88 apply (zenon_L528_); trivial. % 5.66/5.88 apply (zenon_L530_); trivial. % 5.66/5.88 apply (zenon_L66_); trivial. % 5.66/5.88 apply (zenon_L20_); trivial. % 5.66/5.88 (* end of lemma zenon_L531_ *) % 5.66/5.88 assert (zenon_L532_ : (((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e0) (e0)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> False). % 5.66/5.88 do 0 intro. intros zenon_H2f zenon_H122 zenon_H17d zenon_H1a5 zenon_H143 zenon_H1e3 zenon_H1e2 zenon_H1c2 zenon_H18e zenon_H1c7 zenon_H55 zenon_H21 zenon_H23 zenon_H195 zenon_H100 zenon_H8e zenon_H57 zenon_H8f zenon_H6d zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hdd zenon_Hf8 zenon_Hee zenon_Hf3 zenon_Hf6 zenon_H113 zenon_H10a zenon_H115 zenon_H114 zenon_H20 zenon_H63 zenon_H45 zenon_H52 zenon_H97 zenon_H105 zenon_H72 zenon_Hed zenon_H9a zenon_Hdc zenon_Hd9 zenon_H1d1 zenon_H11f zenon_H1ad zenon_H86 zenon_H169 zenon_Hde zenon_H158 zenon_H11d zenon_H11e zenon_H189 zenon_H118 zenon_H188. % 5.66/5.88 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H22. zenon_intro zenon_H30. % 5.66/5.88 apply (zenon_L531_); trivial. % 5.66/5.88 (* end of lemma zenon_L532_ *) % 5.66/5.88 assert (zenon_L533_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (~((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)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.66/5.88 do 0 intro. intros zenon_Hde zenon_H118 zenon_H11a zenon_H59 zenon_H1e2 zenon_H97 zenon_H86 zenon_Hca zenon_H1e3 zenon_H11f zenon_H1ad zenon_H6d zenon_H3d zenon_H2c zenon_H52. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.88 apply (zenon_L16_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.88 apply (zenon_L87_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.88 apply (zenon_L58_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.88 apply (zenon_L305_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.88 apply (zenon_L89_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.88 apply (zenon_L90_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.88 apply (zenon_L92_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.88 apply (zenon_L377_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.88 apply (zenon_L190_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.88 apply (zenon_L93_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.88 apply (zenon_L62_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.88 apply (zenon_L310_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.88 apply (zenon_L484_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.88 apply (zenon_L94_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.88 apply (zenon_L63_); trivial. % 5.66/5.88 apply (zenon_L284_); trivial. % 5.66/5.88 (* end of lemma zenon_L533_ *) % 5.66/5.88 assert (zenon_L534_ : (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((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) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> ((op (e0) (e3)) = (e0)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((e0) = (e3))) -> ((op (e1) (e1)) = (e1)) -> (~((e0) = (e1))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e3))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.88 do 0 intro. intros zenon_H185 zenon_H1f2 zenon_H59 zenon_H1e2 zenon_H52 zenon_H1e6 zenon_Hde zenon_H3d zenon_H1ad zenon_H11f zenon_H1e3 zenon_H97 zenon_H11a zenon_H118 zenon_H6d zenon_H2c zenon_Hee zenon_H63 zenon_H86 zenon_H9d zenon_H3e zenon_H39 zenon_H58. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H185); [ zenon_intro zenon_H182 | zenon_intro zenon_H186 ]. % 5.66/5.88 apply (zenon_L468_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_Haf | zenon_intro zenon_H187 ]. % 5.66/5.88 apply (zenon_L424_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H15e | zenon_intro zenon_H5f ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1e4 ]. % 5.66/5.88 apply (zenon_L491_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1e5 ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H1e6); [ zenon_intro zenon_Hca | zenon_intro zenon_H1e7 ]. % 5.66/5.88 apply (zenon_L533_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H1e7); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H1e8 ]. % 5.66/5.88 apply (zenon_L350_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H60 ]. % 5.66/5.88 apply (zenon_L485_); trivial. % 5.66/5.88 exact (zenon_H3e zenon_H60). % 5.66/5.88 apply (zenon_or_s _ _ zenon_H1e5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H61 ]. % 5.66/5.88 apply (zenon_L369_); trivial. % 5.66/5.88 exact (zenon_H59 zenon_H61). % 5.66/5.88 exact (zenon_H58 zenon_H5f). % 5.66/5.88 (* end of lemma zenon_L534_ *) % 5.66/5.88 assert (zenon_L535_ : ((op (e2) (e3)) = (e1)) -> ((op (e0) (e0)) = (e2)) -> ((op (e3) (e3)) = (e0)) -> False). % 5.66/5.88 do 0 intro. intros zenon_H144 zenon_H16c zenon_H5b. % 5.66/5.88 apply (zenon_notand_s _ _ ax8); [ zenon_intro zenon_H5c | zenon_intro zenon_H210 ]. % 5.66/5.88 apply zenon_H5c. apply sym_equal. exact zenon_H5b. % 5.66/5.88 apply (zenon_notand_s _ _ zenon_H210); [ zenon_intro zenon_H20b | zenon_intro zenon_H1b4 ]. % 5.66/5.88 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.88 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e2) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.88 intro zenon_D_pnotp. % 5.66/5.88 apply zenon_H20b. % 5.66/5.88 rewrite <- zenon_D_pnotp. % 5.66/5.88 exact zenon_H1b6. % 5.66/5.88 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.88 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20c]. % 5.66/5.88 congruence. % 5.66/5.88 cut (((op (e0) (e0)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 5.66/5.88 intro zenon_D_pnotp. % 5.66/5.88 apply zenon_H20c. % 5.66/5.88 rewrite <- zenon_D_pnotp. % 5.66/5.88 exact zenon_H16c. % 5.66/5.88 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.88 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 5.66/5.88 congruence. % 5.66/5.88 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.88 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.88 intro zenon_D_pnotp. % 5.66/5.88 apply zenon_H1fc. % 5.66/5.88 rewrite <- zenon_D_pnotp. % 5.66/5.88 exact zenon_H1b6. % 5.66/5.88 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.88 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 5.66/5.88 congruence. % 5.66/5.88 apply (zenon_L452_); trivial. % 5.66/5.88 apply zenon_H1b7. apply refl_equal. % 5.66/5.88 apply zenon_H1b7. apply refl_equal. % 5.66/5.88 apply zenon_H62. apply refl_equal. % 5.66/5.88 apply zenon_H1b7. apply refl_equal. % 5.66/5.88 apply zenon_H1b7. apply refl_equal. % 5.66/5.88 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.66/5.88 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((e1) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.66/5.88 intro zenon_D_pnotp. % 5.66/5.88 apply zenon_H1b4. % 5.66/5.88 rewrite <- zenon_D_pnotp. % 5.66/5.88 exact zenon_H1ba. % 5.66/5.88 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.66/5.88 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 5.66/5.88 congruence. % 5.66/5.88 cut (((op (e2) (e3)) = (e1)) = ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e1))). % 5.66/5.88 intro zenon_D_pnotp. % 5.66/5.88 apply zenon_H1bc. % 5.66/5.88 rewrite <- zenon_D_pnotp. % 5.66/5.88 exact zenon_H144. % 5.66/5.88 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.66/5.88 cut (((op (e2) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 5.66/5.88 congruence. % 5.66/5.88 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.66/5.88 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((op (e2) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.66/5.88 intro zenon_D_pnotp. % 5.66/5.88 apply zenon_H20e. % 5.66/5.88 rewrite <- zenon_D_pnotp. % 5.66/5.88 exact zenon_H1ba. % 5.66/5.88 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.66/5.88 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (e2) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 5.66/5.88 congruence. % 5.66/5.88 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.66/5.88 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H20c]. % 5.66/5.88 congruence. % 5.66/5.88 cut (((op (e0) (e0)) = (e2)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e2))). % 5.66/5.88 intro zenon_D_pnotp. % 5.66/5.88 apply zenon_H20c. % 5.66/5.88 rewrite <- zenon_D_pnotp. % 5.66/5.88 exact zenon_H16c. % 5.66/5.88 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.66/5.88 cut (((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 5.66/5.88 congruence. % 5.66/5.88 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.66/5.88 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e0) (e0)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.66/5.88 intro zenon_D_pnotp. % 5.66/5.88 apply zenon_H1fc. % 5.66/5.88 rewrite <- zenon_D_pnotp. % 5.66/5.88 exact zenon_H1b6. % 5.66/5.88 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.66/5.88 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e0) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 5.66/5.88 congruence. % 5.66/5.88 apply (zenon_L452_); trivial. % 5.66/5.88 apply zenon_H1b7. apply refl_equal. % 5.66/5.88 apply zenon_H1b7. apply refl_equal. % 5.66/5.88 apply zenon_H62. apply refl_equal. % 5.66/5.88 apply zenon_H6f. apply refl_equal. % 5.66/5.88 apply zenon_H1bb. apply refl_equal. % 5.66/5.88 apply zenon_H1bb. apply refl_equal. % 5.66/5.88 apply zenon_H94. apply refl_equal. % 5.66/5.88 apply zenon_H1bb. apply refl_equal. % 5.66/5.88 apply zenon_H1bb. apply refl_equal. % 5.66/5.88 (* end of lemma zenon_L535_ *) % 5.66/5.88 assert (zenon_L536_ : (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((op (e0) (e0)) = (e2)) -> ((op (e2) (e3)) = (e1)) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> False). % 5.66/5.88 do 0 intro. intros zenon_H55 zenon_H16c zenon_H144 zenon_H58 zenon_H59 zenon_H3e. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 5.66/5.88 apply (zenon_L535_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 5.66/5.88 exact (zenon_H58 zenon_H5f). % 5.66/5.88 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H61 | zenon_intro zenon_H60 ]. % 5.66/5.88 exact (zenon_H59 zenon_H61). % 5.66/5.88 exact (zenon_H3e zenon_H60). % 5.66/5.88 (* end of lemma zenon_L536_ *) % 5.66/5.88 assert (zenon_L537_ : (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> ((op (e0) (e0)) = (e2)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.66/5.88 do 0 intro. intros zenon_H171 zenon_Hb3 zenon_H9d zenon_H97 zenon_H52 zenon_H45 zenon_H25 zenon_H31 zenon_H63 zenon_H105 zenon_H3e zenon_H59 zenon_H16c zenon_H55 zenon_H58. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H14a | zenon_intro zenon_H172 ]. % 5.66/5.88 apply (zenon_L272_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_H173 ]. % 5.66/5.88 apply (zenon_L75_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H144 | zenon_intro zenon_H5f ]. % 5.66/5.88 apply (zenon_L536_); trivial. % 5.66/5.88 exact (zenon_H58 zenon_H5f). % 5.66/5.88 (* end of lemma zenon_L537_ *) % 5.66/5.88 assert (zenon_L538_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e2) = (e3))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e0)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((e1) = (e3))) -> ((op (e0) (e3)) = (e3)) -> False). % 5.66/5.88 do 0 intro. intros zenon_H14f zenon_H150 zenon_H86 zenon_H63 zenon_H97 zenon_H171 zenon_H52 zenon_H45 zenon_H25 zenon_H31 zenon_H105 zenon_H3e zenon_H59 zenon_H55 zenon_H58 zenon_H169 zenon_Hee zenon_H33 zenon_H9d zenon_Hb3. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.88 exact (zenon_H150 zenon_H152). % 5.66/5.88 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.88 apply (zenon_L537_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.88 apply (zenon_L155_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.88 apply (zenon_L176_); trivial. % 5.66/5.88 apply (zenon_L401_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.88 apply (zenon_L480_); trivial. % 5.66/5.88 apply (zenon_L272_); trivial. % 5.66/5.88 (* end of lemma zenon_L538_ *) % 5.66/5.88 assert (zenon_L539_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e0)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> False). % 5.66/5.88 do 0 intro. intros zenon_Haa zenon_H26 zenon_H16c zenon_Hf0 zenon_Hd6 zenon_H55 zenon_H57 zenon_H58 zenon_H59 zenon_H3e zenon_H154 zenon_H33 zenon_Hf8 zenon_H77 zenon_H9d zenon_Hee zenon_H146 zenon_H1d1 zenon_H97 zenon_H42 zenon_H25 zenon_H52 zenon_Hd9 zenon_H86. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hab ]. % 5.66/5.88 apply (zenon_L102_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H2d | zenon_intro zenon_Hac ]. % 5.66/5.88 exact (zenon_H26 zenon_H2d). % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha6 ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H12b | zenon_intro zenon_H147 ]. % 5.66/5.88 apply (zenon_L121_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H148 ]. % 5.66/5.88 apply (zenon_L41_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H47 | zenon_intro zenon_H144 ]. % 5.66/5.88 exact (zenon_H77 zenon_H47). % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H3d | zenon_intro zenon_Hfb ]. % 5.66/5.88 apply (zenon_L136_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H56 | zenon_intro zenon_Hfc ]. % 5.66/5.88 apply (zenon_L13_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H65 | zenon_intro zenon_H5b ]. % 5.66/5.88 apply (zenon_L68_); trivial. % 5.66/5.88 apply (zenon_L535_); trivial. % 5.66/5.88 apply (zenon_L371_); trivial. % 5.66/5.88 (* end of lemma zenon_L539_ *) % 5.66/5.88 assert (zenon_L540_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e3)) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.66/5.88 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_H105 zenon_H45 zenon_H171 zenon_H63 zenon_Hb3 zenon_H9d zenon_H33 zenon_Hee zenon_H169 zenon_Hd9 zenon_H25 zenon_H1d1 zenon_H146 zenon_H77 zenon_Hf8 zenon_H154 zenon_H3e zenon_H59 zenon_H58 zenon_H57 zenon_H55 zenon_Hf0 zenon_H26 zenon_Haa zenon_H97 zenon_H11f zenon_H52 zenon_H86 zenon_H150 zenon_H14f zenon_H6d zenon_Hca. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.66/5.88 exact (zenon_H20 zenon_H1f). % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.66/5.88 apply (zenon_L538_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.88 exact (zenon_H150 zenon_H152). % 5.66/5.88 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.66/5.88 apply (zenon_L539_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.66/5.88 apply (zenon_L155_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.66/5.88 apply (zenon_L187_); trivial. % 5.66/5.88 apply (zenon_L401_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.88 apply (zenon_L480_); trivial. % 5.66/5.88 apply (zenon_L272_); trivial. % 5.66/5.88 apply (zenon_L304_); trivial. % 5.66/5.88 (* end of lemma zenon_L540_ *) % 5.66/5.88 assert (zenon_L541_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e3))) -> False). % 5.66/5.88 do 0 intro. intros zenon_Hc8 zenon_H16e zenon_H16a zenon_H14f zenon_H150 zenon_H86 zenon_H52 zenon_H11f zenon_H97 zenon_Haa zenon_H26 zenon_Hf0 zenon_H55 zenon_H57 zenon_H58 zenon_H59 zenon_H3e zenon_H154 zenon_Hf8 zenon_H77 zenon_H146 zenon_H1d1 zenon_H25 zenon_Hd9 zenon_H169 zenon_Hee zenon_H9d zenon_H63 zenon_H171 zenon_H45 zenon_H105 zenon_Hf6 zenon_H6d. % 5.66/5.88 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.66/5.88 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.66/5.88 exact (zenon_H20 zenon_H1f). % 5.66/5.88 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.66/5.88 apply (zenon_L509_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.66/5.88 apply (zenon_L540_); trivial. % 5.66/5.88 apply (zenon_L271_); trivial. % 5.66/5.88 (* end of lemma zenon_L541_ *) % 5.66/5.88 assert (zenon_L542_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e3))) -> False). % 5.66/5.88 do 0 intro. intros zenon_Hc8 zenon_H16e zenon_H16a zenon_H14f zenon_H150 zenon_H86 zenon_H52 zenon_H11f zenon_H97 zenon_Haa zenon_H26 zenon_Hf0 zenon_H55 zenon_H57 zenon_H58 zenon_H59 zenon_H3e zenon_H154 zenon_Hf8 zenon_H77 zenon_H146 zenon_H1d1 zenon_H25 zenon_Hd9 zenon_H169 zenon_Hee zenon_H9d zenon_H63 zenon_H171 zenon_H45 zenon_H105 zenon_Hf6 zenon_H6d. % 5.66/5.88 apply (zenon_L541_); trivial. % 5.66/5.88 (* end of lemma zenon_L542_ *) % 5.66/5.88 assert (zenon_L543_ : (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((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 (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 5.66/5.88 do 0 intro. intros zenon_H105 zenon_H97 zenon_H25 zenon_H45 zenon_H52 zenon_H8e zenon_H9d zenon_H41 zenon_H26 zenon_H1ef zenon_Hd3 zenon_H86. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.66/5.88 apply (zenon_L333_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.66/5.88 exact (zenon_H25 zenon_H2e). % 5.66/5.88 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.66/5.88 apply (zenon_L74_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.66/5.88 apply (zenon_L99_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.66/5.88 exact (zenon_H26 zenon_H2d). % 5.66/5.88 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.66/5.88 apply (zenon_L414_); trivial. % 5.66/5.88 apply (zenon_L398_); trivial. % 5.66/5.88 (* end of lemma zenon_L543_ *) % 5.66/5.88 assert (zenon_L544_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((e2) = (e3))) -> False). % 5.66/5.88 do 0 intro. intros zenon_H3f zenon_H105 zenon_H97 zenon_H25 zenon_H45 zenon_H52 zenon_H8e zenon_H9d zenon_H26 zenon_H1ef zenon_Hd3 zenon_H86. % 5.66/5.88 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.66/5.88 apply (zenon_L543_); trivial. % 5.66/5.88 (* end of lemma zenon_L544_ *) % 5.66/5.88 assert (zenon_L545_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (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))))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.66/5.88 do 0 intro. intros zenon_Hde zenon_H58 zenon_H1f2 zenon_Hee zenon_H185 zenon_H86 zenon_H1ef zenon_H26 zenon_H9d zenon_H8e zenon_H45 zenon_H25 zenon_H97 zenon_H105 zenon_H11a zenon_H188 zenon_H11f zenon_H2c zenon_H1ad zenon_Hf3 zenon_Hd3 zenon_H1a0 zenon_H52. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.88 apply (zenon_L16_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.88 apply (zenon_L87_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.88 apply (zenon_L58_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.88 apply (zenon_L487_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.88 apply (zenon_L544_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.88 apply (zenon_L90_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.88 apply (zenon_L92_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.88 apply (zenon_L421_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.88 apply (zenon_L190_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.88 apply (zenon_L93_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.88 apply (zenon_L62_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.88 apply (zenon_L310_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.88 apply (zenon_L279_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.88 apply (zenon_L281_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.88 apply (zenon_L63_); trivial. % 5.66/5.88 apply (zenon_L284_); trivial. % 5.66/5.88 (* end of lemma zenon_L545_ *) % 5.66/5.88 assert (zenon_L546_ : (((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). % 5.66/5.88 do 0 intro. intros zenon_H1e3 zenon_H63 zenon_H39 zenon_Ha6 zenon_H86 zenon_H52 zenon_H1e2 zenon_H59. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1e4 ]. % 5.66/5.88 apply (zenon_L491_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1e5 ]. % 5.66/5.88 apply (zenon_L350_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H1e5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H61 ]. % 5.66/5.88 apply (zenon_L369_); trivial. % 5.66/5.88 exact (zenon_H59 zenon_H61). % 5.66/5.88 (* end of lemma zenon_L546_ *) % 5.66/5.88 assert (zenon_L547_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e3)) = (e2))) -> False). % 5.66/5.88 do 0 intro. intros zenon_H3b zenon_H1e3 zenon_H63 zenon_Ha6 zenon_H86 zenon_H52 zenon_H1e2 zenon_H59. % 5.66/5.88 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.66/5.88 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.66/5.88 apply (zenon_L546_); trivial. % 5.66/5.88 (* end of lemma zenon_L547_ *) % 5.66/5.88 assert (zenon_L548_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> False). % 5.66/5.88 do 0 intro. intros zenon_H3f zenon_H1d1 zenon_H97 zenon_H25 zenon_H52 zenon_Hd9 zenon_H86 zenon_Ha6. % 5.66/5.88 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.66/5.88 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.66/5.88 apply (zenon_L371_); trivial. % 5.66/5.88 (* end of lemma zenon_L548_ *) % 5.66/5.88 assert (zenon_L549_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e2))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> False). % 5.66/5.88 do 0 intro. intros zenon_H1a0 zenon_H2c zenon_H25 zenon_Ha6 zenon_H122 zenon_H17d zenon_H1a5 zenon_H143 zenon_H1e3 zenon_H1e2 zenon_H1c2 zenon_H18e zenon_H1c7 zenon_H55 zenon_H21 zenon_H23 zenon_H195 zenon_H100 zenon_H8e zenon_H57 zenon_H8f zenon_H6d zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hdd zenon_Hf8 zenon_Hee zenon_Hf3 zenon_Hf6 zenon_H113 zenon_H10a zenon_H115 zenon_H114 zenon_H63 zenon_H45 zenon_H52 zenon_H97 zenon_H105 zenon_H72 zenon_Hed zenon_H9a zenon_Hdc zenon_Hd9 zenon_H1d1 zenon_H11f zenon_H1ad zenon_H86 zenon_H169 zenon_Hde zenon_H158 zenon_H11d zenon_H11e zenon_H189 zenon_H118 zenon_H188 zenon_H20. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.88 apply (zenon_L16_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.88 apply (zenon_L532_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.88 apply (zenon_L58_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.88 apply (zenon_L547_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.88 apply (zenon_L548_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.88 apply (zenon_L90_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.88 apply (zenon_L59_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.88 apply (zenon_L295_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.88 apply (zenon_L190_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.88 apply (zenon_L61_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.88 apply (zenon_L62_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.88 apply (zenon_L310_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.88 apply (zenon_L299_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.88 apply (zenon_L94_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.88 apply (zenon_L63_); trivial. % 5.66/5.88 apply (zenon_L284_); trivial. % 5.66/5.88 apply (zenon_L280_); trivial. % 5.66/5.88 (* end of lemma zenon_L549_ *) % 5.66/5.88 assert (zenon_L550_ : (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((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) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 5.66/5.88 do 0 intro. intros zenon_Hb8 zenon_H20 zenon_H188 zenon_H118 zenon_H189 zenon_H185 zenon_H11e zenon_H11a zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H14b zenon_H14f zenon_H146 zenon_H140 zenon_H126 zenon_H123 zenon_H129 zenon_H12a zenon_H163 zenon_H16e zenon_H179 zenon_H171 zenon_H174 zenon_Hde zenon_H169 zenon_H86 zenon_H1ad zenon_H11f zenon_H1d1 zenon_Hd9 zenon_Hdc zenon_H9a zenon_Hed zenon_H72 zenon_H105 zenon_H97 zenon_H52 zenon_H45 zenon_H63 zenon_H114 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf6 zenon_Hf3 zenon_Hee zenon_Hf0 zenon_Hf8 zenon_Hdd zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_H117 zenon_H6d zenon_H8f zenon_H4a zenon_H57 zenon_H8e zenon_Hfd zenon_H100 zenon_H195 zenon_H23 zenon_H21 zenon_H55 zenon_H1c7 zenon_H18e zenon_H1c2 zenon_H1e2 zenon_H1e3 zenon_H143 zenon_H1a5 zenon_H17d zenon_H122 zenon_H1f2 zenon_H2c zenon_H150 zenon_H77 zenon_H26 zenon_H1e6 zenon_H25 zenon_H16a zenon_H1ef zenon_H1a0. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.66/5.88 apply (zenon_L16_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.66/5.88 apply (zenon_L532_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.66/5.88 apply (zenon_L58_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.66/5.88 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.66/5.88 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.66/5.88 apply (zenon_L534_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.66/5.88 apply (zenon_L89_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.66/5.88 apply (zenon_L90_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.66/5.88 apply (zenon_L59_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.66/5.88 apply (zenon_L421_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.66/5.88 apply (zenon_L190_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.66/5.88 apply (zenon_L61_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.66/5.88 apply (zenon_L62_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.66/5.88 apply (zenon_L310_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.66/5.88 apply (zenon_L542_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.66/5.88 apply (zenon_L94_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.66/5.88 apply (zenon_L63_); trivial. % 5.66/5.88 apply (zenon_L284_); trivial. % 5.66/5.88 apply (zenon_L222_); trivial. % 5.66/5.88 apply (zenon_L545_); trivial. % 5.66/5.88 apply (zenon_L549_); trivial. % 5.66/5.88 (* end of lemma zenon_L550_ *) % 5.66/5.88 assert (zenon_L551_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((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 (e3) (e3)) = (e3))) -> False). % 5.66/5.88 do 0 intro. intros zenon_H14f zenon_H150 zenon_H6d zenon_Hc2 zenon_H86 zenon_H26 zenon_H9d zenon_Haa zenon_H63 zenon_H13f zenon_H140 zenon_Hee zenon_H33 zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.66/5.88 exact (zenon_H150 zenon_H152). % 5.66/5.88 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.66/5.88 apply (zenon_L385_); trivial. % 5.66/5.88 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.66/5.88 apply (zenon_L480_); trivial. % 5.66/5.88 apply (zenon_L292_); trivial. % 5.66/5.88 (* end of lemma zenon_L551_ *) % 5.66/5.88 assert (zenon_L552_ : (((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e1))) -> (((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 (e3) (e3)) = (e3))) -> False). % 5.66/5.88 do 0 intro. intros zenon_H36 zenon_H14f zenon_H150 zenon_H6d zenon_Hc2 zenon_H86 zenon_H26 zenon_H9d zenon_Haa zenon_H63 zenon_H13f zenon_H140 zenon_Hee zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.66/5.88 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.66/5.88 apply (zenon_L551_); trivial. % 5.66/5.88 (* end of lemma zenon_L552_ *) % 5.66/5.88 assert (zenon_L553_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 5.74/5.89 do 0 intro. intros zenon_Hde zenon_H72 zenon_Hed zenon_H118 zenon_H11a zenon_H9d zenon_H86 zenon_H110 zenon_H25 zenon_H22 zenon_H63 zenon_H1d1 zenon_Hc2 zenon_H129 zenon_H143 zenon_H2c zenon_Ha6 zenon_H1a0. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.89 apply (zenon_L16_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.89 apply (zenon_L87_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.89 apply (zenon_L31_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.89 apply (zenon_L449_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.89 apply (zenon_L89_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.89 apply (zenon_L90_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.89 apply (zenon_L92_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.89 apply (zenon_L295_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.89 apply (zenon_L475_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.89 apply (zenon_L93_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.89 apply (zenon_L51_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.89 apply (zenon_L379_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.89 apply (zenon_L299_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.89 apply (zenon_L94_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.89 apply (zenon_L303_); trivial. % 5.74/5.89 apply (zenon_L284_); trivial. % 5.74/5.89 (* end of lemma zenon_L553_ *) % 5.74/5.89 assert (zenon_L554_ : (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 5.74/5.89 do 0 intro. intros zenon_Haa zenon_H6d zenon_H26 zenon_Hcd zenon_Hde zenon_H72 zenon_Hed zenon_H118 zenon_H11a zenon_H9d zenon_H86 zenon_H110 zenon_H25 zenon_H22 zenon_H63 zenon_H1d1 zenon_Hc2 zenon_H129 zenon_H143 zenon_H2c zenon_H1a0. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hab ]. % 5.74/5.89 apply (zenon_L40_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H2d | zenon_intro zenon_Hac ]. % 5.74/5.89 exact (zenon_H26 zenon_H2d). % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha6 ]. % 5.74/5.89 apply (zenon_L317_); trivial. % 5.74/5.89 apply (zenon_L553_); trivial. % 5.74/5.89 (* end of lemma zenon_L554_ *) % 5.74/5.89 assert (zenon_L555_ : (((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))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> ((op (e2) (e3)) = (e3)) -> False). % 5.74/5.89 do 0 intro. intros zenon_H18e zenon_H108 zenon_Hc2 zenon_H63 zenon_H4b zenon_H6d zenon_Hcd. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H18f ]. % 5.74/5.89 apply (zenon_L100_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H12f | zenon_intro zenon_H190 ]. % 5.74/5.89 apply (zenon_L349_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H4f | zenon_intro zenon_H65 ]. % 5.74/5.89 exact (zenon_H4b zenon_H4f). % 5.74/5.89 apply (zenon_L326_); trivial. % 5.74/5.89 (* end of lemma zenon_L555_ *) % 5.74/5.89 assert (zenon_L556_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e3) (e1)) = (e1)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e1)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.74/5.89 do 0 intro. intros zenon_H14f zenon_H150 zenon_Haf zenon_H123 zenon_Hee zenon_H33 zenon_H95 zenon_H14b. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.74/5.89 exact (zenon_H150 zenon_H152). % 5.74/5.89 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.74/5.89 apply (zenon_L194_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.74/5.89 apply (zenon_L480_); trivial. % 5.74/5.89 apply (zenon_L134_); trivial. % 5.74/5.89 (* end of lemma zenon_L556_ *) % 5.74/5.89 assert (zenon_L557_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.74/5.89 do 0 intro. intros zenon_Had zenon_H14f zenon_H150 zenon_H123 zenon_Hee zenon_H33 zenon_H14b. % 5.74/5.89 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.74/5.89 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.74/5.89 apply (zenon_L556_); trivial. % 5.74/5.89 (* end of lemma zenon_L557_ *) % 5.74/5.89 assert (zenon_L558_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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 (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((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))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> False). % 5.74/5.89 do 0 intro. intros zenon_H179 zenon_Hde zenon_Hf3 zenon_H143 zenon_H11f zenon_H4d zenon_H13f zenon_H63 zenon_Haa zenon_H86 zenon_H26 zenon_H140 zenon_H185 zenon_H97 zenon_H1f2 zenon_H110 zenon_H14f zenon_H14b zenon_H33 zenon_H123 zenon_H116 zenon_Hc2 zenon_H129 zenon_H4b zenon_H45 zenon_H4c zenon_H4a zenon_H6d zenon_H1cb zenon_Hca zenon_H9d zenon_Hee zenon_H118 zenon_H150 zenon_H2c. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.89 apply (zenon_L16_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.89 apply (zenon_L87_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.89 apply (zenon_L501_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.89 apply (zenon_L305_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.89 apply (zenon_L89_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.89 apply (zenon_L90_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.89 apply (zenon_L143_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.89 apply (zenon_L557_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.89 apply (zenon_L117_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.89 apply (zenon_L93_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.89 apply (zenon_L51_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.89 apply (zenon_L426_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.89 apply (zenon_L420_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.89 apply (zenon_L307_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.89 apply (zenon_L308_); trivial. % 5.74/5.89 apply (zenon_L284_); trivial. % 5.74/5.89 apply (zenon_L298_); trivial. % 5.74/5.89 (* end of lemma zenon_L558_ *) % 5.74/5.89 assert (zenon_L559_ : (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e2)) = (e0)) -> False). % 5.74/5.89 do 0 intro. intros zenon_H1a6 zenon_H33 zenon_H74. % 5.74/5.89 cut (((op (e0) (e2)) = (e0)) = ((op (e0) (e2)) = (op (e1) (e2)))). % 5.74/5.89 intro zenon_D_pnotp. % 5.74/5.89 apply zenon_H1a6. % 5.74/5.89 rewrite <- zenon_D_pnotp. % 5.74/5.89 exact zenon_H33. % 5.74/5.89 cut (((e0) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H211]. % 5.74/5.89 cut (((op (e0) (e2)) = (op (e0) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 5.74/5.89 congruence. % 5.74/5.89 apply zenon_H121. apply refl_equal. % 5.74/5.89 apply zenon_H211. apply sym_equal. exact zenon_H74. % 5.74/5.89 (* end of lemma zenon_L559_ *) % 5.74/5.89 assert (zenon_L560_ : ((op (e1) (e3)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> ((op (e3) (e3)) = (e2)) -> False). % 5.74/5.89 do 0 intro. intros zenon_H56 zenon_H47 zenon_H61. % 5.74/5.89 apply (zenon_notand_s _ _ ax20); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H212 ]. % 5.74/5.89 apply zenon_H1b3. apply sym_equal. exact zenon_H61. % 5.74/5.89 apply (zenon_notand_s _ _ zenon_H212); [ zenon_intro zenon_H1fa | zenon_intro zenon_H20a ]. % 5.74/5.89 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.74/5.89 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((e1) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.74/5.89 intro zenon_D_pnotp. % 5.74/5.89 apply zenon_H1fa. % 5.74/5.89 rewrite <- zenon_D_pnotp. % 5.74/5.89 exact zenon_H1b6. % 5.74/5.89 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.74/5.89 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 5.74/5.89 congruence. % 5.74/5.89 cut (((op (e2) (e2)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 5.74/5.89 intro zenon_D_pnotp. % 5.74/5.89 apply zenon_H1fb. % 5.74/5.89 rewrite <- zenon_D_pnotp. % 5.74/5.89 exact zenon_H47. % 5.74/5.89 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.74/5.89 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b9]. % 5.74/5.89 congruence. % 5.74/5.89 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.74/5.89 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.74/5.89 intro zenon_D_pnotp. % 5.74/5.89 apply zenon_H1b9. % 5.74/5.89 rewrite <- zenon_D_pnotp. % 5.74/5.89 exact zenon_H1b6. % 5.74/5.89 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.74/5.89 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 5.74/5.89 congruence. % 5.74/5.89 apply (zenon_L323_); trivial. % 5.74/5.89 apply zenon_H1b7. apply refl_equal. % 5.74/5.89 apply zenon_H1b7. apply refl_equal. % 5.74/5.89 apply zenon_H94. apply refl_equal. % 5.74/5.89 apply zenon_H1b7. apply refl_equal. % 5.74/5.89 apply zenon_H1b7. apply refl_equal. % 5.74/5.89 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.74/5.89 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((e0) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.74/5.89 intro zenon_D_pnotp. % 5.74/5.89 apply zenon_H20a. % 5.74/5.89 rewrite <- zenon_D_pnotp. % 5.74/5.89 exact zenon_H1ba. % 5.74/5.89 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.74/5.89 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H20d]. % 5.74/5.89 congruence. % 5.74/5.89 cut (((op (e1) (e3)) = (e0)) = ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (e0))). % 5.74/5.89 intro zenon_D_pnotp. % 5.74/5.89 apply zenon_H20d. % 5.74/5.89 rewrite <- zenon_D_pnotp. % 5.74/5.89 exact zenon_H56. % 5.74/5.89 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.74/5.89 cut (((op (e1) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 5.74/5.89 congruence. % 5.74/5.89 elim (classic ((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [ zenon_intro zenon_H1ba | zenon_intro zenon_H1bb ]. % 5.74/5.89 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3))) = ((op (e1) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))). % 5.74/5.89 intro zenon_D_pnotp. % 5.74/5.89 apply zenon_H1fd. % 5.74/5.89 rewrite <- zenon_D_pnotp. % 5.74/5.89 exact zenon_H1ba. % 5.74/5.89 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (op (op (e3) (e3)) (op (e3) (e3))) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1bb]. % 5.74/5.89 cut (((op (op (op (e3) (e3)) (op (e3) (e3))) (e3)) = (op (e1) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H1fe]. % 5.74/5.89 congruence. % 5.74/5.89 cut (((e3) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 5.74/5.89 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 5.74/5.89 congruence. % 5.74/5.89 cut (((op (e2) (e2)) = (e1)) = ((op (op (e3) (e3)) (op (e3) (e3))) = (e1))). % 5.74/5.89 intro zenon_D_pnotp. % 5.74/5.89 apply zenon_H1fb. % 5.74/5.89 rewrite <- zenon_D_pnotp. % 5.74/5.89 exact zenon_H47. % 5.74/5.89 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.74/5.89 cut (((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b9]. % 5.74/5.89 congruence. % 5.74/5.89 elim (classic ((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [ zenon_intro zenon_H1b6 | zenon_intro zenon_H1b7 ]. % 5.74/5.89 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3)))) = ((op (e2) (e2)) = (op (op (e3) (e3)) (op (e3) (e3))))). % 5.74/5.89 intro zenon_D_pnotp. % 5.74/5.89 apply zenon_H1b9. % 5.74/5.89 rewrite <- zenon_D_pnotp. % 5.74/5.89 exact zenon_H1b6. % 5.74/5.89 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (op (e3) (e3)) (op (e3) (e3))))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 5.74/5.89 cut (((op (op (e3) (e3)) (op (e3) (e3))) = (op (e2) (e2)))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 5.74/5.89 congruence. % 5.74/5.89 apply (zenon_L323_); trivial. % 5.74/5.89 apply zenon_H1b7. apply refl_equal. % 5.74/5.89 apply zenon_H1b7. apply refl_equal. % 5.74/5.89 apply zenon_H94. apply refl_equal. % 5.74/5.89 apply zenon_H6f. apply refl_equal. % 5.74/5.89 apply zenon_H1bb. apply refl_equal. % 5.74/5.89 apply zenon_H1bb. apply refl_equal. % 5.74/5.89 apply zenon_H67. apply refl_equal. % 5.74/5.89 apply zenon_H1bb. apply refl_equal. % 5.74/5.89 apply zenon_H1bb. apply refl_equal. % 5.74/5.89 (* end of lemma zenon_L560_ *) % 5.74/5.89 assert (zenon_L561_ : (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e0) (e3)) = (e1)) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e3)) -> ((op (e1) (e3)) = (e0)) -> ((op (e2) (e2)) = (e1)) -> False). % 5.74/5.89 do 0 intro. intros zenon_H1bf zenon_H97 zenon_H14a zenon_H63 zenon_H86 zenon_Hcd zenon_H56 zenon_H47. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H1bf); [ zenon_intro zenon_H167 | zenon_intro zenon_H1c0 ]. % 5.74/5.89 apply (zenon_L321_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H1c0); [ zenon_intro zenon_H96 | zenon_intro zenon_H1c1 ]. % 5.74/5.89 apply (zenon_L322_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H1c1); [ zenon_intro zenon_H64 | zenon_intro zenon_H61 ]. % 5.74/5.89 apply (zenon_L282_); trivial. % 5.74/5.89 apply (zenon_L560_); trivial. % 5.74/5.89 (* end of lemma zenon_L561_ *) % 5.74/5.89 assert (zenon_L562_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((op (e2) (e1)) = (e2)) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((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) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> ((op (e2) (e3)) = (e3)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (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) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.74/5.89 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_H150 zenon_H118 zenon_H1cb zenon_H6d zenon_H4a zenon_H4c zenon_H45 zenon_H4b zenon_H129 zenon_Hc2 zenon_H116 zenon_H123 zenon_H33 zenon_H14b zenon_H14f zenon_H110 zenon_H97 zenon_H140 zenon_H26 zenon_H86 zenon_Haa zenon_H63 zenon_H13f zenon_H4d zenon_H11f zenon_H143 zenon_Hf3 zenon_Hde zenon_H179 zenon_H18e zenon_Hcd zenon_H17d zenon_H1a6 zenon_H146 zenon_H11a zenon_H1bf zenon_Hb8 zenon_H10a zenon_H185 zenon_Hee zenon_H2c zenon_H1f2 zenon_Hd3 zenon_H9d zenon_H58. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.74/5.89 exact (zenon_H20 zenon_H1f). % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.74/5.89 exact (zenon_Hb8 zenon_Hba). % 5.74/5.89 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.74/5.89 apply (zenon_L19_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.74/5.89 apply (zenon_L555_); trivial. % 5.74/5.89 apply (zenon_L558_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.74/5.89 exact (zenon_H150 zenon_H152). % 5.74/5.89 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.74/5.89 apply (zenon_L385_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.74/5.89 apply (zenon_L133_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.74/5.89 exact (zenon_Hb8 zenon_Hba). % 5.74/5.89 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.74/5.89 apply (zenon_L19_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.74/5.89 exact (zenon_H13f zenon_H28). % 5.74/5.89 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.74/5.89 apply (zenon_L559_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H146); [ zenon_intro zenon_H12b | zenon_intro zenon_H147 ]. % 5.74/5.89 apply (zenon_L121_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H148 ]. % 5.74/5.89 apply (zenon_L91_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H148); [ zenon_intro zenon_H47 | zenon_intro zenon_H144 ]. % 5.74/5.89 apply (zenon_L561_); trivial. % 5.74/5.89 apply (zenon_L430_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.74/5.89 apply (zenon_L555_); trivial. % 5.74/5.89 apply (zenon_L558_); trivial. % 5.74/5.89 apply (zenon_L486_); trivial. % 5.74/5.89 (* end of lemma zenon_L562_ *) % 5.74/5.89 assert (zenon_L563_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e1) (e1)) = (e0))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e1))) -> False). % 5.74/5.89 do 0 intro. intros zenon_H3b zenon_H14f zenon_H150 zenon_H143 zenon_H1d1 zenon_H97 zenon_H25 zenon_H63 zenon_H86 zenon_Ha6 zenon_H13f zenon_H140 zenon_H4d zenon_H4c zenon_H11f zenon_H4b zenon_H4a zenon_Hee. % 5.74/5.89 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.74/5.89 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.74/5.89 apply (zenon_L353_); trivial. % 5.74/5.89 (* end of lemma zenon_L563_ *) % 5.74/5.89 assert (zenon_L564_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((e2) = (e3))) -> ((op (e2) (e3)) = (e2)) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((op (e2) (e2)) = (e0))) -> (~((e0) = (e3))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (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))) -> False). % 5.74/5.89 do 0 intro. intros zenon_H3b zenon_H14f zenon_H150 zenon_H143 zenon_H1d1 zenon_H25 zenon_H140 zenon_H14b zenon_H1e9 zenon_H4c zenon_H17d zenon_H122 zenon_H13f zenon_H86 zenon_H64 zenon_H185 zenon_Hee zenon_Ha6 zenon_H9d zenon_H97 zenon_H202 zenon_H146 zenon_H63 zenon_H4b zenon_H6d zenon_H18e zenon_H77 zenon_H10d zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59. % 5.74/5.89 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.74/5.89 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.74/5.89 apply (zenon_L504_); trivial. % 5.74/5.89 (* end of lemma zenon_L564_ *) % 5.74/5.89 assert (zenon_L565_ : (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 5.74/5.89 do 0 intro. intros zenon_H20 zenon_H188 zenon_H118 zenon_H189 zenon_H185 zenon_H11e zenon_H11a zenon_H11d zenon_H158 zenon_H179 zenon_Hde zenon_H169 zenon_H86 zenon_H1ad zenon_H11f zenon_H1d1 zenon_Hd9 zenon_Hdc zenon_H9a zenon_Hed zenon_H72 zenon_H105 zenon_H97 zenon_H52 zenon_H45 zenon_H63 zenon_H114 zenon_H115 zenon_H10a zenon_H113 zenon_Hf6 zenon_Hf3 zenon_Hee zenon_Hf8 zenon_Hdd zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H9d zenon_H6d zenon_H8f zenon_H57 zenon_H8e zenon_H100 zenon_H195 zenon_H23 zenon_H21 zenon_H55 zenon_H1c7 zenon_H18e zenon_H1c2 zenon_H1e2 zenon_H1e3 zenon_H143 zenon_H1a5 zenon_H17d zenon_H122 zenon_H1f2 zenon_H2c zenon_H26 zenon_H3d zenon_H1e6 zenon_H16a zenon_H25 zenon_H1ef zenon_H1a0. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.89 apply (zenon_L16_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.89 apply (zenon_L532_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.89 apply (zenon_L58_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.89 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.74/5.89 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.74/5.89 apply (zenon_L534_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.89 apply (zenon_L200_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.89 apply (zenon_L90_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.89 apply (zenon_L59_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.89 apply (zenon_L421_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.89 apply (zenon_L190_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.89 apply (zenon_L61_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.89 apply (zenon_L62_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.89 apply (zenon_L310_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.89 apply (zenon_L484_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.89 apply (zenon_L94_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.89 apply (zenon_L63_); trivial. % 5.74/5.89 apply (zenon_L284_); trivial. % 5.74/5.89 apply (zenon_L545_); trivial. % 5.74/5.89 apply (zenon_L549_); trivial. % 5.74/5.89 (* end of lemma zenon_L565_ *) % 5.74/5.89 assert (zenon_L566_ : (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e3)) = (e0)) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> False). % 5.74/5.89 do 0 intro. intros zenon_H1e9 zenon_H1d1 zenon_H1a0 zenon_H1c7 zenon_H1cb zenon_H198 zenon_H189 zenon_H169 zenon_H16e zenon_H179 zenon_H174 zenon_H16a zenon_H18e zenon_H202 zenon_H195 zenon_H158 zenon_H11e zenon_H100 zenon_Hfd zenon_H57 zenon_H72 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9f zenon_Ha7 zenon_Haa zenon_Hce zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hed zenon_Hf3 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H129 zenon_H12a zenon_H20 zenon_H2c zenon_H11f zenon_H4a zenon_H122 zenon_H13f zenon_H45 zenon_H14b zenon_H3d zenon_H17d zenon_H118 zenon_H11a zenon_H188 zenon_H14f zenon_Hb4 zenon_H55 zenon_H105 zenon_H163 zenon_H9d zenon_H6d zenon_H26 zenon_H86 zenon_H171 zenon_H97 zenon_H1bf zenon_Hee zenon_H8e zenon_H25 zenon_H63 zenon_Hb7 zenon_H150 zenon_Hf6 zenon_H1f2 zenon_H185 zenon_H146 zenon_H1ef zenon_H1ff zenon_H4b zenon_H8f zenon_Hde zenon_H1a5 zenon_H1ad zenon_H1c2 zenon_H1e2 zenon_H1e3 zenon_H1e6. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.89 apply (zenon_L16_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.89 apply (zenon_L87_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.89 apply (zenon_L313_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.89 apply (zenon_L483_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.89 apply (zenon_L89_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.89 apply (zenon_L90_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.89 apply (zenon_L92_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.89 apply (zenon_L421_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.89 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.74/5.89 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.74/5.89 apply (zenon_L463_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.89 apply (zenon_L93_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.89 apply (zenon_L51_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.89 apply (zenon_L472_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.89 apply (zenon_L484_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.89 apply (zenon_L94_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.89 apply (zenon_L348_); trivial. % 5.74/5.89 apply (zenon_L284_); trivial. % 5.74/5.89 apply (zenon_L229_); trivial. % 5.74/5.89 apply (zenon_L347_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.89 apply (zenon_L16_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.89 apply (zenon_L87_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.89 apply (zenon_L313_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.89 apply (zenon_L563_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.89 apply (zenon_L89_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.89 apply (zenon_L90_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.89 apply (zenon_L92_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.89 apply (zenon_L295_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.89 apply (zenon_L478_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.89 apply (zenon_L93_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.89 apply (zenon_L51_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.89 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.74/5.89 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.74/5.89 apply (zenon_L498_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.89 apply (zenon_L299_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.89 apply (zenon_L94_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.89 apply (zenon_L303_); trivial. % 5.74/5.89 apply (zenon_L284_); trivial. % 5.74/5.89 apply (zenon_L42_); trivial. % 5.74/5.89 apply (zenon_L280_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.89 apply (zenon_L16_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.89 apply (zenon_L87_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.89 apply (zenon_L501_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.89 apply (zenon_L305_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.89 apply (zenon_L89_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.89 apply (zenon_L90_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.89 apply (zenon_L92_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.89 apply (zenon_L421_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.89 apply (zenon_L502_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.89 apply (zenon_L93_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.89 apply (zenon_L51_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.89 apply (zenon_L426_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.89 apply (zenon_L484_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.89 apply (zenon_L307_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.89 apply (zenon_L308_); trivial. % 5.74/5.89 apply (zenon_L284_); trivial. % 5.74/5.89 apply (zenon_L298_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.89 apply (zenon_L503_); trivial. % 5.74/5.89 apply (zenon_L231_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.89 apply (zenon_L16_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.89 apply (zenon_L87_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.89 apply (zenon_L147_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.89 apply (zenon_L487_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.89 apply (zenon_L166_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.89 apply (zenon_L90_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.89 apply (zenon_L92_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.89 apply (zenon_L421_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.89 apply (zenon_L173_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.89 apply (zenon_L93_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.89 apply (zenon_L51_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.89 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.74/5.89 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.74/5.89 exact (zenon_H20 zenon_H1f). % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.74/5.89 apply (zenon_L467_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.74/5.89 apply (zenon_L146_); trivial. % 5.74/5.89 apply (zenon_L486_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.89 apply (zenon_L279_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.89 apply (zenon_L281_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.89 apply (zenon_L283_); trivial. % 5.74/5.89 apply (zenon_L284_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.89 apply (zenon_L16_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.89 apply (zenon_L87_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.89 apply (zenon_L147_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.89 apply (zenon_L564_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.89 apply (zenon_L89_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.89 apply (zenon_L90_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.89 apply (zenon_L92_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.89 apply (zenon_L421_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.89 apply (zenon_L173_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.89 apply (zenon_L138_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.89 apply (zenon_L51_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.89 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.74/5.89 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.74/5.89 apply (zenon_L498_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.89 apply (zenon_L484_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.89 apply (zenon_L94_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.89 apply (zenon_L303_); trivial. % 5.74/5.89 apply (zenon_L284_); trivial. % 5.74/5.89 apply (zenon_L280_); trivial. % 5.74/5.89 apply (zenon_L506_); trivial. % 5.74/5.89 apply (zenon_L565_); trivial. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.89 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.89 apply (zenon_L396_); trivial. % 5.74/5.89 apply (zenon_L118_); trivial. % 5.74/5.89 apply (zenon_L60_); trivial. % 5.74/5.89 (* end of lemma zenon_L566_ *) % 5.74/5.89 assert (zenon_L567_ : (~((op (e3) (e3)) = (e1))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> ((op (e2) (e3)) = (e3)) -> (~((op (e2) (e2)) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e2))\/(((op (e1) (e2)) = (e2))\/(((op (e2) (e2)) = (e2))\/((op (e3) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((op (e0) (e2)) = (op (e3) (e2)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((e1) = (e3))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e1) = (e2))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e3)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H58 zenon_Hd3 zenon_Hb8 zenon_H1a6 zenon_Hcd zenon_H4d zenon_Hc2 zenon_H4c zenon_H1e9 zenon_H1d1 zenon_H1a0 zenon_H1c7 zenon_H1cb zenon_H198 zenon_H189 zenon_H169 zenon_H16e zenon_H179 zenon_H174 zenon_H16a zenon_H18e zenon_H202 zenon_H195 zenon_H158 zenon_H11e zenon_H100 zenon_Hfd zenon_H57 zenon_H72 zenon_H9a zenon_H117 zenon_Hd9 zenon_H9f zenon_Ha7 zenon_Haa zenon_Hce zenon_Hdc zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hed zenon_Hf3 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H155 zenon_H154 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H129 zenon_H12a zenon_H20 zenon_H2c zenon_H11f zenon_H4a zenon_H122 zenon_H13f zenon_H45 zenon_H14b zenon_H17d zenon_H118 zenon_H11a zenon_H188 zenon_H14f zenon_Hb4 zenon_H55 zenon_H105 zenon_H163 zenon_H9d zenon_H6d zenon_H26 zenon_H86 zenon_H171 zenon_H97 zenon_H1bf zenon_Hee zenon_H8e zenon_H25 zenon_H63 zenon_Hb7 zenon_H150 zenon_Hf6 zenon_H1f2 zenon_H185 zenon_H146 zenon_H1ef zenon_H1ff zenon_H4b zenon_H8f zenon_Hde zenon_H1a5 zenon_H1ad zenon_H1c2 zenon_H1e2 zenon_H1e3 zenon_H1e6. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.74/5.90 exact (zenon_H20 zenon_H1f). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.74/5.90 apply (zenon_L554_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.74/5.90 apply (zenon_L562_); trivial. % 5.74/5.90 apply (zenon_L566_); trivial. % 5.74/5.90 (* end of lemma zenon_L567_ *) % 5.74/5.90 assert (zenon_L568_ : (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e1) (e2)) = (e1)) -> False). % 5.74/5.90 do 0 intro. intros zenon_H213 zenon_H2c zenon_H46. % 5.74/5.90 cut (((op (e1) (e1)) = (e1)) = ((op (e1) (e1)) = (op (e1) (e2)))). % 5.74/5.90 intro zenon_D_pnotp. % 5.74/5.90 apply zenon_H213. % 5.74/5.90 rewrite <- zenon_D_pnotp. % 5.74/5.90 exact zenon_H2c. % 5.74/5.90 cut (((e1) = (op (e1) (e2)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 5.74/5.90 cut (((op (e1) (e1)) = (op (e1) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 5.74/5.90 congruence. % 5.74/5.90 apply zenon_H11c. apply refl_equal. % 5.74/5.90 apply zenon_Ha0. apply sym_equal. exact zenon_H46. % 5.74/5.90 (* end of lemma zenon_L568_ *) % 5.74/5.90 assert (zenon_L569_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((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))))) -> (((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 (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e3) (e2)) = (e3)) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e2)) = (e3))) -> (((op (e0) (e3)) = (e2))\/(((op (e1) (e3)) = (e2))\/(((op (e2) (e3)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (op (e1) (e2)))) -> ((op (e1) (e1)) = (e1)) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (~((op (e0) (e2)) = (op (e1) (e2)))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e3))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H14f zenon_H26 zenon_Haa zenon_H140 zenon_H1cb zenon_H150 zenon_H118 zenon_H10a zenon_Hb8 zenon_Hd3 zenon_H10d zenon_Hc2 zenon_H4d zenon_H1bf zenon_H97 zenon_H63 zenon_H86 zenon_H213 zenon_H2c zenon_H33 zenon_Hee zenon_H163 zenon_H1a6 zenon_H13f zenon_H17d zenon_H6d zenon_Hd6 zenon_H9d. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.74/5.90 exact (zenon_H150 zenon_H152). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.74/5.90 apply (zenon_L385_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.74/5.90 apply (zenon_L480_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.74/5.90 exact (zenon_H150 zenon_H152). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.74/5.90 apply (zenon_L88_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.74/5.90 apply (zenon_L121_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.74/5.90 exact (zenon_Hb8 zenon_Hba). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.74/5.90 apply (zenon_L19_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.74/5.90 exact (zenon_H13f zenon_H28). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.74/5.90 apply (zenon_L559_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H149 | zenon_intro zenon_H164 ]. % 5.74/5.90 apply (zenon_L480_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H46 | zenon_intro zenon_H165 ]. % 5.74/5.90 apply (zenon_L568_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H47 | zenon_intro zenon_H15e ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H10d); [ zenon_intro zenon_H108 | zenon_intro zenon_H10e ]. % 5.74/5.90 apply (zenon_L100_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H10e); [ zenon_intro zenon_Ha4 | zenon_intro zenon_H10f ]. % 5.74/5.90 apply (zenon_L114_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H10f); [ zenon_intro zenon_H51 | zenon_intro zenon_Hcd ]. % 5.74/5.90 exact (zenon_H4d zenon_H51). % 5.74/5.90 apply (zenon_L561_); trivial. % 5.74/5.90 apply (zenon_L485_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.74/5.90 apply (zenon_L100_); trivial. % 5.74/5.90 apply (zenon_L339_); trivial. % 5.74/5.90 (* end of lemma zenon_L569_ *) % 5.74/5.90 assert (zenon_L570_ : ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((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 (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((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))))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((e0) = (e3))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> False). % 5.74/5.90 do 0 intro. intros zenon_H179 zenon_Hde zenon_Hf3 zenon_H143 zenon_H14f zenon_H11f zenon_H4d zenon_H13f zenon_H63 zenon_Haa zenon_H86 zenon_H26 zenon_H140 zenon_H185 zenon_H97 zenon_H1f2 zenon_H110 zenon_H188 zenon_H116 zenon_Hc2 zenon_H129 zenon_H4b zenon_H45 zenon_H4c zenon_H4a zenon_H6d zenon_H1cb zenon_Hca zenon_H9d zenon_Hee zenon_H118 zenon_H150 zenon_H2c. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.90 apply (zenon_L16_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.90 apply (zenon_L87_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.90 apply (zenon_L501_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.90 apply (zenon_L305_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.90 apply (zenon_L89_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.90 apply (zenon_L90_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.90 apply (zenon_L143_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.90 apply (zenon_L421_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.90 apply (zenon_L117_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.90 apply (zenon_L93_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.90 apply (zenon_L51_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.90 apply (zenon_L426_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.90 apply (zenon_L420_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.90 apply (zenon_L307_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.90 apply (zenon_L308_); trivial. % 5.74/5.90 apply (zenon_L284_); trivial. % 5.74/5.90 apply (zenon_L298_); trivial. % 5.74/5.90 (* end of lemma zenon_L570_ *) % 5.74/5.90 assert (zenon_L571_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((op (e3) (e2)) = (e3)) -> (~((e1) = (e3))) -> (~((op (e3) (e3)) = (e1))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_Hf3 zenon_H86 zenon_H6d zenon_Hb8 zenon_H10a zenon_Hbe zenon_H63 zenon_H185 zenon_Hee zenon_H2c zenon_H1f2 zenon_Hd3 zenon_H9d zenon_H58. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.74/5.90 exact (zenon_H20 zenon_H1f). % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.74/5.90 apply (zenon_L319_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.74/5.90 apply (zenon_L320_); trivial. % 5.74/5.90 apply (zenon_L486_); trivial. % 5.74/5.90 (* end of lemma zenon_L571_ *) % 5.74/5.90 assert (zenon_L572_ : (~((op (e3) (e1)) = (op (e3) (e2)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e3) (e0)) = (e3))\/(((op (e3) (e1)) = (e3))\/(((op (e3) (e2)) = (e3))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e3))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H1a0 zenon_H1ef zenon_H16a zenon_H25 zenon_H1e6 zenon_H26 zenon_H150 zenon_H2c zenon_H1f2 zenon_H122 zenon_H17d zenon_H1a5 zenon_H143 zenon_H1e3 zenon_H1e2 zenon_H1c2 zenon_H18e zenon_H1c7 zenon_H55 zenon_H21 zenon_H23 zenon_H195 zenon_H100 zenon_Hfd zenon_H8e zenon_H57 zenon_H4a zenon_H8f zenon_H6d zenon_H117 zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hdd zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H114 zenon_H63 zenon_H45 zenon_H52 zenon_H97 zenon_H105 zenon_H72 zenon_Hed zenon_H9a zenon_Hdc zenon_Hd9 zenon_H1d1 zenon_H11f zenon_H1ad zenon_H86 zenon_H169 zenon_Hde zenon_H174 zenon_H171 zenon_H179 zenon_H16e zenon_H163 zenon_H12a zenon_H129 zenon_H123 zenon_H126 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H118 zenon_H188 zenon_H20 zenon_Hb8. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.90 apply (zenon_L550_); trivial. % 5.74/5.90 apply (zenon_L60_); trivial. % 5.74/5.90 (* end of lemma zenon_L572_ *) % 5.74/5.90 assert (zenon_L573_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> False). % 5.74/5.90 do 0 intro. intros zenon_H3b zenon_H154 zenon_H33. % 5.74/5.90 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.74/5.90 apply (zenon_L136_); trivial. % 5.74/5.90 (* end of lemma zenon_L573_ *) % 5.74/5.90 assert (zenon_L574_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e3))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hc8 zenon_Hf6 zenon_H105 zenon_H45 zenon_H171 zenon_H63 zenon_H9d zenon_H33 zenon_Hee zenon_H169 zenon_Hd9 zenon_H25 zenon_H1d1 zenon_H146 zenon_H77 zenon_Hf8 zenon_H154 zenon_H3e zenon_H59 zenon_H58 zenon_H57 zenon_H55 zenon_Hf0 zenon_H26 zenon_Haa zenon_H97 zenon_H11f zenon_H52 zenon_H86 zenon_H150 zenon_H14f zenon_H6d. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.74/5.90 apply (zenon_L540_); trivial. % 5.74/5.90 (* end of lemma zenon_L574_ *) % 5.74/5.90 assert (zenon_L575_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (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) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e2))) -> (~((e1) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e1) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((e0) = (e3))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hc8 zenon_Hf6 zenon_H105 zenon_H45 zenon_H171 zenon_H63 zenon_H9d zenon_H33 zenon_Hee zenon_H169 zenon_Hd9 zenon_H25 zenon_H1d1 zenon_H146 zenon_H77 zenon_Hf8 zenon_H154 zenon_H3e zenon_H59 zenon_H58 zenon_H57 zenon_H55 zenon_Hf0 zenon_H26 zenon_Haa zenon_H97 zenon_H11f zenon_H52 zenon_H86 zenon_H150 zenon_H14f zenon_H6d. % 5.74/5.90 apply (zenon_L574_); trivial. % 5.74/5.90 (* end of lemma zenon_L575_ *) % 5.74/5.90 assert (zenon_L576_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((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) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (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) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> ((op (e1) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (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) (e2)) = (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 (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H195 zenon_H194 zenon_H17d zenon_H174 zenon_H179 zenon_H16e zenon_H163 zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H14b zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H21 zenon_H23 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf3 zenon_Hed zenon_Hdd zenon_Hdc zenon_Hce zenon_Hb7 zenon_Hb4 zenon_Ha7 zenon_H9f zenon_H117 zenon_H9a zenon_H8f zenon_H4a zenon_H72 zenon_H8e zenon_Hfd zenon_H100 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H18a zenon_H32 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H2c zenon_H52 zenon_H33 zenon_H154 zenon_H118 zenon_H188 zenon_H11f zenon_Hd9 zenon_H1ad zenon_Hf6 zenon_H6d zenon_H26 zenon_H146 zenon_H57 zenon_Hf0 zenon_Hf8 zenon_H77 zenon_H1d1 zenon_Haa zenon_H150 zenon_H169 zenon_H86 zenon_H9d zenon_H105 zenon_H97 zenon_H45 zenon_H25 zenon_H63 zenon_H55 zenon_H171 zenon_Hee zenon_H14f zenon_Hde zenon_H1a0 zenon_H1a5. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.90 apply (zenon_L16_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.90 apply (zenon_L87_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.90 apply (zenon_L58_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.90 apply (zenon_L573_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.90 apply (zenon_L89_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.90 apply (zenon_L90_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.90 apply (zenon_L59_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.90 apply (zenon_L421_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.90 apply (zenon_L190_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.90 apply (zenon_L61_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.90 apply (zenon_L62_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.90 apply (zenon_L310_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.90 apply (zenon_L575_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.90 apply (zenon_L94_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.90 apply (zenon_L63_); trivial. % 5.74/5.90 apply (zenon_L284_); trivial. % 5.74/5.90 apply (zenon_L263_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.90 apply (zenon_L16_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.90 apply (zenon_L87_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.90 apply (zenon_L58_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.90 apply (zenon_L573_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.90 apply (zenon_L89_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.90 apply (zenon_L90_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.90 apply (zenon_L92_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.90 apply (zenon_L421_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.90 apply (zenon_L109_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.90 apply (zenon_L93_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.90 apply (zenon_L62_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.90 apply (zenon_L310_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.90 apply (zenon_L279_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.90 apply (zenon_L281_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.90 apply (zenon_L63_); trivial. % 5.74/5.90 apply (zenon_L284_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.90 apply (zenon_L16_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.90 apply (zenon_L87_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.90 apply (zenon_L58_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.90 apply (zenon_L573_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.90 apply (zenon_L548_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.90 apply (zenon_L90_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.90 apply (zenon_L59_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.90 apply (zenon_L421_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.90 apply (zenon_L190_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.90 apply (zenon_L61_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.90 apply (zenon_L62_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.90 apply (zenon_L310_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.90 apply (zenon_L299_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.90 apply (zenon_L94_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.90 apply (zenon_L63_); trivial. % 5.74/5.90 apply (zenon_L284_); trivial. % 5.74/5.90 (* end of lemma zenon_L576_ *) % 5.74/5.90 assert (zenon_L577_ : ((~((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 (e2) (e2)) = (e0))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> ((op (e2) (e1)) = (e2)) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H195 zenon_H126 zenon_H4b zenon_H4c zenon_H4d zenon_H4a zenon_H123 zenon_H122 zenon_Ha7 zenon_Hce zenon_H10d zenon_H2c zenon_H118 zenon_H45 zenon_H129 zenon_H116 zenon_H110 zenon_Hde zenon_H150 zenon_H140 zenon_H9d zenon_H26 zenon_H86 zenon_H6d zenon_Haa zenon_Hc2 zenon_H63 zenon_H13f zenon_Hee zenon_H33 zenon_H55 zenon_H59 zenon_Hb4 zenon_Hf7 zenon_H14f. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.90 apply (zenon_L551_); trivial. % 5.74/5.90 apply (zenon_L148_); trivial. % 5.74/5.90 (* end of lemma zenon_L577_ *) % 5.74/5.90 assert (zenon_L578_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> (((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 (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hc5 zenon_H169 zenon_H16a zenon_H63 zenon_H22 zenon_H198 zenon_H174. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.74/5.90 apply (zenon_L358_); trivial. % 5.74/5.90 (* end of lemma zenon_L578_ *) % 5.74/5.90 assert (zenon_L579_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e3))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((e2) = (e3))) -> (~((e1) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e1) = (e3))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hc8 zenon_H14f zenon_H3e zenon_H59 zenon_H58 zenon_H57 zenon_H55 zenon_H4a zenon_H45 zenon_H77 zenon_H4c zenon_H4d zenon_H13f zenon_H105 zenon_H25 zenon_H14b zenon_H26 zenon_H8e zenon_Hf8 zenon_H6d zenon_Hce zenon_H17d zenon_Hee zenon_H86 zenon_H97 zenon_H22 zenon_H63 zenon_H16a zenon_H169 zenon_H9d. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.74/5.90 apply (zenon_L473_); trivial. % 5.74/5.90 (* end of lemma zenon_L579_ *) % 5.74/5.90 assert (zenon_L580_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> (~((e1) = (e2))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((op (e0) (e1)) = (e0)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> ((op (e0) (e2)) = (e2)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (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 (e3) (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) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((op (e2) (e0)) = (e2)) -> (~((e0) = (e2))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_H9d zenon_H97 zenon_H11e zenon_H118 zenon_Hdd zenon_H9a zenon_H23 zenon_H22 zenon_H21 zenon_H9f zenon_H114 zenon_Hb7 zenon_Hb8 zenon_Hb0 zenon_H105 zenon_H25 zenon_H14b zenon_H86 zenon_H26 zenon_H8e zenon_Hf8 zenon_H57 zenon_H3e zenon_H59 zenon_H58 zenon_Hce zenon_H55 zenon_H1cb zenon_Hbe zenon_H63 zenon_H6d zenon_Hca. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.74/5.90 exact (zenon_H20 zenon_H1f). % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.74/5.90 exact (zenon_Hb8 zenon_Hba). % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.74/5.90 apply (zenon_L40_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.74/5.90 apply (zenon_L45_); trivial. % 5.74/5.90 apply (zenon_L454_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.74/5.90 apply (zenon_L530_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.74/5.90 apply (zenon_L338_); trivial. % 5.74/5.90 apply (zenon_L339_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.74/5.90 apply (zenon_L320_); trivial. % 5.74/5.90 apply (zenon_L304_); trivial. % 5.74/5.90 (* end of lemma zenon_L580_ *) % 5.74/5.90 assert (zenon_L581_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e1)) = (op (e3) (e1)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> ((op (e2) (e0)) = (e2)) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((e1) = (e2))) -> (~((e0) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (e1))) -> (~((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (e3))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((e0) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((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)) = (e1)) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H1cb zenon_H1a5 zenon_H1f2 zenon_Hde zenon_H146 zenon_Hf6 zenon_H169 zenon_H16a zenon_H9d zenon_Hf0 zenon_Hbe zenon_H14f zenon_Hb4 zenon_H97 zenon_Hee zenon_Hb8 zenon_H6d zenon_H86 zenon_H17d zenon_H45 zenon_H77 zenon_H4c zenon_H4d zenon_H4a zenon_H13f zenon_H63 zenon_H25 zenon_H8e zenon_H14b zenon_H26 zenon_Hf8 zenon_Hce zenon_H57 zenon_H55 zenon_H105 zenon_Hb7 zenon_H188 zenon_H11a zenon_H118 zenon_Hed zenon_H72 zenon_H22 zenon_H2c zenon_H20 zenon_H193 zenon_H191 zenon_H18c zenon_H18e zenon_H32 zenon_H18a zenon_H189 zenon_H185 zenon_H11e zenon_H100 zenon_Hfd zenon_H8f zenon_H9a zenon_H117 zenon_Hd9 zenon_H9f zenon_Ha7 zenon_Haa zenon_Hdc zenon_Hdd zenon_Hf3 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H23 zenon_H21 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H154 zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H11f zenon_H163 zenon_H16e zenon_H179 zenon_H171 zenon_H174 zenon_H194 zenon_H195 zenon_H1d1 zenon_H1a0. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.90 apply (zenon_L460_); trivial. % 5.74/5.90 apply (zenon_L263_); trivial. % 5.74/5.90 apply (zenon_L571_); trivial. % 5.74/5.90 apply (zenon_L476_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.90 apply (zenon_L16_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.90 apply (zenon_L87_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.90 apply (zenon_L31_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.90 apply (zenon_L305_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.90 apply (zenon_L89_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.90 apply (zenon_L90_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.90 apply (zenon_L92_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.90 apply (zenon_L421_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.74/5.90 apply (zenon_L580_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.90 apply (zenon_L83_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.90 apply (zenon_L51_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.90 apply (zenon_L426_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.74/5.90 apply (zenon_L459_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.90 apply (zenon_L307_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.90 apply (zenon_L308_); trivial. % 5.74/5.90 apply (zenon_L284_); trivial. % 5.74/5.90 apply (zenon_L72_); trivial. % 5.74/5.90 apply (zenon_L278_); trivial. % 5.74/5.90 apply (zenon_L298_); trivial. % 5.74/5.90 (* end of lemma zenon_L581_ *) % 5.74/5.90 assert (zenon_L582_ : (((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3))))) -> (((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 (e3) (e2)))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hc5 zenon_H169 zenon_H16a zenon_H63 zenon_H22 zenon_H198 zenon_H174. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.74/5.90 apply (zenon_L358_); trivial. % 5.74/5.90 (* end of lemma zenon_L582_ *) % 5.74/5.90 assert (zenon_L583_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (((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))) -> (~((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). % 5.74/5.90 do 0 intro. intros zenon_Hc8 zenon_Hf8 zenon_H6d zenon_H58 zenon_H97 zenon_Hee zenon_H9d zenon_H171 zenon_H64 zenon_H63 zenon_Hf7. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.74/5.90 apply (zenon_L274_); trivial. % 5.74/5.90 (* end of lemma zenon_L583_ *) % 5.74/5.90 assert (zenon_L584_ : (((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))) -> (~((e2) = (e3))) -> ((op (e2) (e1)) = (e2)) -> (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Haa zenon_H6d zenon_H22 zenon_H26 zenon_H86 zenon_Hc2 zenon_Hc8 zenon_H143. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hab ]. % 5.74/5.90 apply (zenon_L40_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_H2d | zenon_intro zenon_Hac ]. % 5.74/5.90 exact (zenon_H26 zenon_H2d). % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hac); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha6 ]. % 5.74/5.90 apply (zenon_L114_); trivial. % 5.74/5.90 apply (zenon_L299_); trivial. % 5.74/5.90 (* end of lemma zenon_L584_ *) % 5.74/5.90 assert (zenon_L585_ : (((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2))))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((e0) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((e1) = (e3))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> ((op (e2) (e1)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e1) (e1)) = (e1)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hd1 zenon_Haa zenon_H6d zenon_H26 zenon_Hde zenon_H72 zenon_Hed zenon_H118 zenon_H11a zenon_H9d zenon_H86 zenon_H110 zenon_H25 zenon_H22 zenon_H63 zenon_H1d1 zenon_Hc2 zenon_H129 zenon_H143 zenon_H2c zenon_H1a0. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.74/5.90 apply (zenon_L554_); trivial. % 5.74/5.90 (* end of lemma zenon_L585_ *) % 5.74/5.90 assert (zenon_L586_ : (~((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))) -> ((op (e1) (e1)) = (e3)) -> False). % 5.74/5.90 do 0 intro. intros zenon_H214 zenon_H2d. % 5.74/5.90 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 5.74/5.90 cut (((op (e1) (e1)) = (e3))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 5.74/5.90 congruence. % 5.74/5.90 exact (zenon_H26 zenon_H2d). % 5.74/5.90 exact (zenon_H26 zenon_H2d). % 5.74/5.90 (* end of lemma zenon_L586_ *) % 5.74/5.90 assert (zenon_L587_ : ((op (e2) (e1)) = (e0)) -> ((op (e3) (e3)) = (e2)) -> ((op (e1) (e1)) = (e3)) -> False). % 5.74/5.90 do 0 intro. intros zenon_H12f zenon_H61 zenon_H2d. % 5.74/5.90 apply (zenon_notand_s _ _ ax28); [ zenon_intro zenon_H216 | zenon_intro zenon_H215 ]. % 5.74/5.90 apply zenon_H216. apply sym_equal. exact zenon_H2d. % 5.74/5.90 apply (zenon_notand_s _ _ zenon_H215); [ zenon_intro zenon_H217 | zenon_intro zenon_H134 ]. % 5.74/5.90 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H136 | zenon_intro zenon_H137 ]. % 5.74/5.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((e2) = (op (op (e1) (e1)) (op (e1) (e1))))). % 5.74/5.90 intro zenon_D_pnotp. % 5.74/5.90 apply zenon_H217. % 5.74/5.90 rewrite <- zenon_D_pnotp. % 5.74/5.90 exact zenon_H136. % 5.74/5.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 5.74/5.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 5.74/5.90 congruence. % 5.74/5.90 cut (((op (e3) (e3)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 5.74/5.90 intro zenon_D_pnotp. % 5.74/5.90 apply zenon_H218. % 5.74/5.90 rewrite <- zenon_D_pnotp. % 5.74/5.90 exact zenon_H61. % 5.74/5.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.74/5.90 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 5.74/5.90 congruence. % 5.74/5.90 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H136 | zenon_intro zenon_H137 ]. % 5.74/5.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 5.74/5.90 intro zenon_D_pnotp. % 5.74/5.90 apply zenon_H219. % 5.74/5.90 rewrite <- zenon_D_pnotp. % 5.74/5.90 exact zenon_H136. % 5.74/5.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 5.74/5.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 5.74/5.90 congruence. % 5.74/5.90 apply (zenon_L586_); trivial. % 5.74/5.90 apply zenon_H137. apply refl_equal. % 5.74/5.90 apply zenon_H137. apply refl_equal. % 5.74/5.90 apply zenon_H62. apply refl_equal. % 5.74/5.90 apply zenon_H137. apply refl_equal. % 5.74/5.90 apply zenon_H137. apply refl_equal. % 5.74/5.90 elim (classic ((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_H13a | zenon_intro zenon_H13b ]. % 5.74/5.90 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1))) = ((e0) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))). % 5.74/5.90 intro zenon_D_pnotp. % 5.74/5.90 apply zenon_H134. % 5.74/5.90 rewrite <- zenon_D_pnotp. % 5.74/5.90 exact zenon_H13a. % 5.74/5.90 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 5.74/5.90 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 5.74/5.90 congruence. % 5.74/5.90 cut (((op (e2) (e1)) = (e0)) = ((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (e0))). % 5.74/5.90 intro zenon_D_pnotp. % 5.74/5.90 apply zenon_H13c. % 5.74/5.90 rewrite <- zenon_D_pnotp. % 5.74/5.90 exact zenon_H12f. % 5.74/5.90 cut (((e0) = (e0))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 5.74/5.90 cut (((op (e2) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 5.74/5.90 congruence. % 5.74/5.90 elim (classic ((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))); [ zenon_intro zenon_H13a | zenon_intro zenon_H13b ]. % 5.74/5.90 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1))) = ((op (e2) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))). % 5.74/5.90 intro zenon_D_pnotp. % 5.74/5.90 apply zenon_H21a. % 5.74/5.90 rewrite <- zenon_D_pnotp. % 5.74/5.90 exact zenon_H13a. % 5.74/5.90 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (op (op (e1) (e1)) (op (e1) (e1))) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 5.74/5.90 cut (((op (op (op (e1) (e1)) (op (e1) (e1))) (e1)) = (op (e2) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 5.74/5.90 congruence. % 5.74/5.90 cut (((e1) = (e1))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 5.74/5.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 5.74/5.90 congruence. % 5.74/5.90 cut (((op (e3) (e3)) = (e2)) = ((op (op (e1) (e1)) (op (e1) (e1))) = (e2))). % 5.74/5.90 intro zenon_D_pnotp. % 5.74/5.90 apply zenon_H218. % 5.74/5.90 rewrite <- zenon_D_pnotp. % 5.74/5.90 exact zenon_H61. % 5.74/5.90 cut (((e2) = (e2))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 5.74/5.90 cut (((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 5.74/5.90 congruence. % 5.74/5.90 elim (classic ((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [ zenon_intro zenon_H136 | zenon_intro zenon_H137 ]. % 5.74/5.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1)))) = ((op (e3) (e3)) = (op (op (e1) (e1)) (op (e1) (e1))))). % 5.74/5.90 intro zenon_D_pnotp. % 5.74/5.90 apply zenon_H219. % 5.74/5.90 rewrite <- zenon_D_pnotp. % 5.74/5.90 exact zenon_H136. % 5.74/5.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (op (e1) (e1)) (op (e1) (e1))))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 5.74/5.90 cut (((op (op (e1) (e1)) (op (e1) (e1))) = (op (e3) (e3)))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 5.74/5.90 congruence. % 5.74/5.90 apply (zenon_L586_); trivial. % 5.74/5.90 apply zenon_H137. apply refl_equal. % 5.74/5.90 apply zenon_H137. apply refl_equal. % 5.74/5.90 apply zenon_H62. apply refl_equal. % 5.74/5.90 apply zenon_H94. apply refl_equal. % 5.74/5.90 apply zenon_H13b. apply refl_equal. % 5.74/5.90 apply zenon_H13b. apply refl_equal. % 5.74/5.90 apply zenon_H67. apply refl_equal. % 5.74/5.90 apply zenon_H13b. apply refl_equal. % 5.74/5.90 apply zenon_H13b. apply refl_equal. % 5.74/5.90 (* end of lemma zenon_L587_ *) % 5.74/5.90 assert (zenon_L588_ : (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((e1) = (e2))) -> ((op (e3) (e1)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e1)) = (e0)) -> False). % 5.74/5.90 do 0 intro. intros zenon_H1e3 zenon_H63 zenon_H39 zenon_H97 zenon_Haf zenon_H52 zenon_H1e2 zenon_H21 zenon_H13f zenon_H24 zenon_H25 zenon_H12f. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1c5 | zenon_intro zenon_H1e4 ]. % 5.74/5.90 apply (zenon_L491_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1e4); [ zenon_intro zenon_H1cf | zenon_intro zenon_H1e5 ]. % 5.74/5.90 apply (zenon_L368_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1e5); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H61 ]. % 5.74/5.90 apply (zenon_L369_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ]. % 5.74/5.90 exact (zenon_H13f zenon_H28). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ]. % 5.74/5.90 exact (zenon_H24 zenon_H2c). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ]. % 5.74/5.90 exact (zenon_H25 zenon_H2e). % 5.74/5.90 apply (zenon_L587_); trivial. % 5.74/5.90 (* end of lemma zenon_L588_ *) % 5.74/5.90 assert (zenon_L589_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e0)) = (e0)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H169 zenon_H16a zenon_H39 zenon_H143 zenon_H1c2 zenon_Hee zenon_H1e3 zenon_H97 zenon_H1e2 zenon_H21 zenon_H13f zenon_H24 zenon_H25 zenon_H140 zenon_H11f zenon_H52 zenon_H3d zenon_H63. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.74/5.90 exact (zenon_H16a zenon_H16c). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.74/5.90 apply (zenon_L357_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.74/5.90 exact (zenon_H13f zenon_H28). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1c2); [ zenon_intro zenon_H42 | zenon_intro zenon_H1c3 ]. % 5.74/5.90 apply (zenon_L155_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H2c | zenon_intro zenon_H1c4 ]. % 5.74/5.90 exact (zenon_H24 zenon_H2c). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Haf ]. % 5.74/5.90 apply (zenon_L122_); trivial. % 5.74/5.90 apply (zenon_L588_); trivial. % 5.74/5.90 apply (zenon_L127_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.74/5.90 apply (zenon_L187_); trivial. % 5.74/5.90 apply (zenon_L163_); trivial. % 5.74/5.90 (* end of lemma zenon_L589_ *) % 5.74/5.90 assert (zenon_L590_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H3b zenon_H169 zenon_H16a zenon_H143 zenon_H1c2 zenon_Hee zenon_H1e3 zenon_H97 zenon_H1e2 zenon_H21 zenon_H13f zenon_H24 zenon_H25 zenon_H140 zenon_H11f zenon_H52 zenon_H63. % 5.74/5.90 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.74/5.90 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.74/5.90 apply (zenon_L589_); trivial. % 5.74/5.90 (* end of lemma zenon_L590_ *) % 5.74/5.90 assert (zenon_L591_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H3b zenon_H1c7 zenon_H16a zenon_H97 zenon_H41 zenon_H52 zenon_H113 zenon_H63. % 5.74/5.90 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.74/5.90 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.74/5.90 exact (zenon_H16a zenon_H16c). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.74/5.90 apply (zenon_L333_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.74/5.90 apply (zenon_L85_); trivial. % 5.74/5.90 apply (zenon_L491_); trivial. % 5.74/5.90 (* end of lemma zenon_L591_ *) % 5.74/5.90 assert (zenon_L592_ : (((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)) -> (~((e2) = (e3))) -> ((op (e0) (e3)) = (e2)) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hb7 zenon_Hb8 zenon_H9d zenon_H42 zenon_H6d zenon_H33 zenon_H86 zenon_H167. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.74/5.90 exact (zenon_Hb8 zenon_Hba). % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.74/5.90 apply (zenon_L102_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.74/5.90 apply (zenon_L103_); trivial. % 5.74/5.90 apply (zenon_L401_); trivial. % 5.74/5.90 (* end of lemma zenon_L592_ *) % 5.74/5.90 assert (zenon_L593_ : (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e3) (e3)) = (e1))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e3) (e3)) = (e0))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((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)) -> (~((e2) = (e3))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H169 zenon_H58 zenon_H55 zenon_H59 zenon_H3e zenon_Hf7 zenon_Hb4 zenon_H171 zenon_H52 zenon_H45 zenon_H25 zenon_H41 zenon_H105 zenon_H97 zenon_H63 zenon_Hb7 zenon_Hb8 zenon_H9d zenon_H42 zenon_H6d zenon_H33 zenon_H86. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_H68 | zenon_intro zenon_H106 ]. % 5.74/5.90 apply (zenon_L333_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_H2e | zenon_intro zenon_H107 ]. % 5.74/5.90 exact (zenon_H25 zenon_H2e). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H107); [ zenon_intro zenon_H73 | zenon_intro zenon_H96 ]. % 5.74/5.90 apply (zenon_L74_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H14a | zenon_intro zenon_H172 ]. % 5.74/5.90 apply (zenon_L292_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H95 | zenon_intro zenon_H173 ]. % 5.74/5.90 apply (zenon_L30_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H144 | zenon_intro zenon_H5f ]. % 5.74/5.90 apply (zenon_L536_); trivial. % 5.74/5.90 exact (zenon_H58 zenon_H5f). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.74/5.90 apply (zenon_L155_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.74/5.90 apply (zenon_L176_); trivial. % 5.74/5.90 apply (zenon_L592_); trivial. % 5.74/5.90 (* end of lemma zenon_L593_ *) % 5.74/5.90 assert (zenon_L594_ : (((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)) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> ((op (e1) (e3)) = (e3)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hb7 zenon_Hb8 zenon_H123 zenon_Ha6 zenon_H6d zenon_H33 zenon_H89 zenon_H14b. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.74/5.90 exact (zenon_Hb8 zenon_Hba). % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.74/5.90 apply (zenon_L391_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.74/5.90 apply (zenon_L103_); trivial. % 5.74/5.90 apply (zenon_L392_); trivial. % 5.74/5.90 (* end of lemma zenon_L594_ *) % 5.74/5.90 assert (zenon_L595_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> (((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)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hcb zenon_Hb7 zenon_Hb8 zenon_H123 zenon_H6d zenon_H33 zenon_H14b. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.74/5.90 apply (zenon_L594_); trivial. % 5.74/5.90 (* end of lemma zenon_L595_ *) % 5.74/5.90 assert (zenon_L596_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e0))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e2))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.74/5.90 do 0 intro. intros zenon_H188 zenon_H118 zenon_H189 zenon_H11e zenon_H11d zenon_H158 zenon_Hde zenon_Hdc zenon_H9a zenon_Hed zenon_H72 zenon_H20 zenon_H114 zenon_H115 zenon_H10a zenon_Hf3 zenon_Hdd zenon_Hce zenon_Ha7 zenon_H9f zenon_H8f zenon_H8e zenon_H100 zenon_H195 zenon_H23 zenon_H21 zenon_H1c7 zenon_H18e zenon_H1c2 zenon_H1e2 zenon_H1e3 zenon_H143 zenon_H1a5 zenon_H17d zenon_H122 zenon_Hb4 zenon_Hf7 zenon_H116 zenon_H4a zenon_H113 zenon_H117 zenon_H1ad zenon_H14f zenon_H150 zenon_H86 zenon_H11f zenon_H97 zenon_Haa zenon_H26 zenon_Hf0 zenon_H55 zenon_H57 zenon_H58 zenon_H59 zenon_H3e zenon_H154 zenon_Hf8 zenon_H77 zenon_H146 zenon_H1d1 zenon_H25 zenon_Hd9 zenon_H169 zenon_Hee zenon_H9d zenon_H63 zenon_H171 zenon_H45 zenon_H105 zenon_Hf6 zenon_H14b zenon_H33 zenon_H6d zenon_H123 zenon_Hb8 zenon_Hb7 zenon_H52. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.90 apply (zenon_L16_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.90 apply (zenon_L532_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.90 apply (zenon_L58_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.90 apply (zenon_L573_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.90 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.74/5.90 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.74/5.90 apply (zenon_L593_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.90 apply (zenon_L9_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.90 apply (zenon_L59_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.90 apply (zenon_L557_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.90 apply (zenon_L109_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.90 apply (zenon_L61_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.90 apply (zenon_L62_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.90 apply (zenon_L310_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.90 apply (zenon_L575_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.90 apply (zenon_L595_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.90 apply (zenon_L63_); trivial. % 5.74/5.90 apply (zenon_L284_); trivial. % 5.74/5.90 (* end of lemma zenon_L596_ *) % 5.74/5.90 assert (zenon_L597_ : (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e2) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.74/5.90 do 0 intro. intros zenon_H1c7 zenon_H16a zenon_H97 zenon_H41 zenon_H52 zenon_H113 zenon_H86 zenon_Hca. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.74/5.90 exact (zenon_H16a zenon_H16c). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.74/5.90 apply (zenon_L333_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.74/5.90 apply (zenon_L85_); trivial. % 5.74/5.90 apply (zenon_L334_); trivial. % 5.74/5.90 (* end of lemma zenon_L597_ *) % 5.74/5.90 assert (zenon_L598_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((e0) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((e2) = (e3))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hde zenon_H26 zenon_H23 zenon_H21 zenon_H63 zenon_H113 zenon_H16a zenon_H1c7 zenon_H1d1 zenon_H9f zenon_H9d zenon_H11f zenon_Hd9 zenon_H1ad zenon_Ha6 zenon_H143 zenon_H86 zenon_H45 zenon_H25 zenon_H41 zenon_H97 zenon_H105 zenon_H52. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.90 apply (zenon_L16_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.90 apply (zenon_L3_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.90 apply (zenon_L58_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.90 apply (zenon_L591_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.90 apply (zenon_L548_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.90 apply (zenon_L9_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.90 apply (zenon_L106_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.90 apply (zenon_L295_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.90 apply (zenon_L190_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.90 apply (zenon_L61_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.90 apply (zenon_L62_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.90 apply (zenon_L310_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.90 apply (zenon_L299_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.90 apply (zenon_L447_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.90 apply (zenon_L63_); trivial. % 5.74/5.90 apply (zenon_L284_); trivial. % 5.74/5.90 (* end of lemma zenon_L598_ *) % 5.74/5.90 assert (zenon_L599_ : (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> ((op (e1) (e0)) = (e1)) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H4b zenon_H20 zenon_H23 zenon_H24 zenon_H25 zenon_H26 zenon_H21 zenon_H52 zenon_H16a zenon_H97 zenon_H41 zenon_H113 zenon_H63 zenon_H1c7 zenon_H114 zenon_H9f zenon_H9a zenon_Hdd zenon_H150 zenon_Hb8 zenon_H122 zenon_H17d zenon_H1a5 zenon_H143 zenon_H1e3 zenon_H1e2 zenon_H1c2 zenon_H18e zenon_H55 zenon_H195 zenon_H100 zenon_Hfd zenon_H8e zenon_H57 zenon_H4a zenon_H8f zenon_H6d zenon_H117 zenon_H9d zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H45 zenon_H105 zenon_H72 zenon_Hed zenon_Hdc zenon_Hd9 zenon_H1d1 zenon_H11f zenon_H1ad zenon_H86 zenon_H169 zenon_Hde zenon_H171 zenon_H179 zenon_H16e zenon_H163 zenon_H12a zenon_H129 zenon_H123 zenon_H126 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H11a zenon_H11e zenon_H189 zenon_H118 zenon_H188 zenon_H1ef. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.90 apply (zenon_L16_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.90 apply (zenon_L3_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.90 apply (zenon_L58_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.90 apply (zenon_L591_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.90 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.74/5.90 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.74/5.90 exact (zenon_H20 zenon_H1f). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.74/5.90 apply (zenon_L529_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.74/5.90 apply (zenon_L596_); trivial. % 5.74/5.90 apply (zenon_L188_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.90 apply (zenon_L9_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.90 apply (zenon_L106_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.90 apply (zenon_L332_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.90 apply (zenon_L190_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.90 apply (zenon_L61_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.90 apply (zenon_L62_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.90 apply (zenon_L310_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.90 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.90 apply (zenon_L597_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.90 apply (zenon_L447_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.90 apply (zenon_L63_); trivial. % 5.74/5.90 apply (zenon_L284_); trivial. % 5.74/5.90 apply (zenon_L220_); trivial. % 5.74/5.90 apply (zenon_L543_); trivial. % 5.74/5.90 apply (zenon_L598_); trivial. % 5.74/5.90 apply (zenon_L597_); trivial. % 5.74/5.90 apply (zenon_L60_); trivial. % 5.74/5.90 (* end of lemma zenon_L599_ *) % 5.74/5.90 assert (zenon_L600_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e0) (e0)) = (e2))) -> (~((e1) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e3))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (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) (e3)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H3f zenon_H4b zenon_H23 zenon_H24 zenon_H25 zenon_H26 zenon_H21 zenon_H52 zenon_H16a zenon_H97 zenon_H113 zenon_H63 zenon_H1c7 zenon_H114 zenon_H9f zenon_H9a zenon_Hdd zenon_H150 zenon_Hb8 zenon_H122 zenon_H17d zenon_H1a5 zenon_H143 zenon_H1e3 zenon_H1e2 zenon_H1c2 zenon_H18e zenon_H55 zenon_H195 zenon_H100 zenon_Hfd zenon_H8e zenon_H57 zenon_H4a zenon_H8f zenon_H6d zenon_H117 zenon_H9d zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hf8 zenon_Hf0 zenon_Hee zenon_Hf3 zenon_Hf6 zenon_H116 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H45 zenon_H105 zenon_H72 zenon_Hed zenon_Hdc zenon_Hd9 zenon_H1d1 zenon_H11f zenon_H1ad zenon_H86 zenon_H169 zenon_Hde zenon_H171 zenon_H179 zenon_H16e zenon_H163 zenon_H12a zenon_H129 zenon_H123 zenon_H126 zenon_H140 zenon_H146 zenon_H14f zenon_H14b zenon_H154 zenon_H155 zenon_H158 zenon_H11d zenon_H11a zenon_H11e zenon_H189 zenon_H118 zenon_H188 zenon_H1ef. % 5.74/5.90 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.74/5.90 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.74/5.90 apply (zenon_L599_); trivial. % 5.74/5.90 (* end of lemma zenon_L600_ *) % 5.74/5.90 assert (zenon_L601_ : ((op (e3) (e1)) = (e1)) -> ((op (e3) (e0)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Haf zenon_H182 zenon_H143. % 5.74/5.90 elim (classic ((op (e3) (e1)) = (op (e3) (e1)))); [ zenon_intro zenon_H1ec | zenon_intro zenon_H1a1 ]. % 5.74/5.90 cut (((op (e3) (e1)) = (op (e3) (e1))) = ((op (e3) (e0)) = (op (e3) (e1)))). % 5.74/5.90 intro zenon_D_pnotp. % 5.74/5.90 apply zenon_H143. % 5.74/5.90 rewrite <- zenon_D_pnotp. % 5.74/5.90 exact zenon_H1ec. % 5.74/5.90 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 5.74/5.90 cut (((op (e3) (e1)) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 5.74/5.90 congruence. % 5.74/5.90 cut (((op (e3) (e1)) = (e1)) = ((op (e3) (e1)) = (op (e3) (e0)))). % 5.74/5.90 intro zenon_D_pnotp. % 5.74/5.90 apply zenon_H21c. % 5.74/5.90 rewrite <- zenon_D_pnotp. % 5.74/5.90 exact zenon_Haf. % 5.74/5.90 cut (((e1) = (op (e3) (e0)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 5.74/5.90 cut (((op (e3) (e1)) = (op (e3) (e1)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 5.74/5.90 congruence. % 5.74/5.90 apply zenon_H1a1. apply refl_equal. % 5.74/5.90 apply zenon_H183. apply sym_equal. exact zenon_H182. % 5.74/5.90 apply zenon_H1a1. apply refl_equal. % 5.74/5.90 apply zenon_H1a1. apply refl_equal. % 5.74/5.90 (* end of lemma zenon_L601_ *) % 5.74/5.90 assert (zenon_L602_ : (((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) (e3)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> ((op (e3) (e1)) = (e1)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> False). % 5.74/5.90 do 0 intro. intros zenon_H1cb zenon_H150 zenon_H9a zenon_Had zenon_Hee zenon_Hd6 zenon_Haf zenon_H143. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.74/5.90 exact (zenon_H150 zenon_H152). % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.74/5.90 apply (zenon_L332_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.74/5.90 apply (zenon_L121_); trivial. % 5.74/5.90 apply (zenon_L601_); trivial. % 5.74/5.90 (* end of lemma zenon_L602_ *) % 5.74/5.90 assert (zenon_L603_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 5.74/5.90 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_H95 zenon_H45 zenon_H105 zenon_Haf zenon_Had zenon_H9a zenon_H150 zenon_H1cb zenon_H169 zenon_H16a zenon_H143 zenon_H1c2 zenon_Hee zenon_H1e3 zenon_H97 zenon_H1e2 zenon_H21 zenon_H13f zenon_H24 zenon_H25 zenon_H140 zenon_H11f zenon_H52 zenon_H3d zenon_H63. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.74/5.90 exact (zenon_H20 zenon_H1f). % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.74/5.90 apply (zenon_L75_); trivial. % 5.74/5.90 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.74/5.90 apply (zenon_L602_); trivial. % 5.74/5.90 apply (zenon_L589_); trivial. % 5.74/5.90 (* end of lemma zenon_L603_ *) % 5.74/5.90 assert (zenon_L604_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (~((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)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e3) (e1)) = (e1)) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 5.74/5.91 do 0 intro. intros zenon_H16e zenon_Hd9 zenon_H1d1 zenon_H14b zenon_H123 zenon_H14f zenon_Hf6 zenon_H20 zenon_H95 zenon_H45 zenon_H105 zenon_Haf zenon_Had zenon_H9a zenon_H150 zenon_H1cb zenon_H169 zenon_H16a zenon_H143 zenon_H1c2 zenon_Hee zenon_H1e3 zenon_H97 zenon_H1e2 zenon_H21 zenon_H13f zenon_H24 zenon_H25 zenon_H140 zenon_H11f zenon_H52 zenon_H63. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.74/5.91 exact (zenon_H20 zenon_H1f). % 5.74/5.91 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.74/5.91 apply (zenon_L507_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.74/5.91 apply (zenon_L556_); trivial. % 5.74/5.91 apply (zenon_L603_); trivial. % 5.74/5.91 (* end of lemma zenon_L604_ *) % 5.74/5.91 assert (zenon_L605_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> ((op (e3) (e1)) = (e3)) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((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)) = (e1))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((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 (e3) (e3)) = (e3))) -> False). % 5.74/5.91 do 0 intro. intros zenon_H14f zenon_H150 zenon_Ha6 zenon_H86 zenon_Hd9 zenon_H52 zenon_H25 zenon_H1d1 zenon_H63 zenon_H3d zenon_H97 zenon_H21 zenon_H13f zenon_H24 zenon_H23 zenon_H26 zenon_H16a zenon_H169 zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.74/5.91 exact (zenon_H150 zenon_H152). % 5.74/5.91 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.74/5.91 apply (zenon_L371_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.74/5.91 exact (zenon_H16a zenon_H16c). % 5.74/5.91 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.74/5.91 apply (zenon_L169_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.74/5.91 apply (zenon_L156_); trivial. % 5.74/5.91 apply (zenon_L163_); trivial. % 5.74/5.91 apply (zenon_L292_); trivial. % 5.74/5.91 (* end of lemma zenon_L605_ *) % 5.74/5.91 assert (zenon_L606_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((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 (e3) (e3)) = (e3))) -> False). % 5.74/5.91 do 0 intro. intros zenon_Hcb zenon_H14f zenon_H150 zenon_H86 zenon_Hd9 zenon_H52 zenon_H25 zenon_H1d1 zenon_H63 zenon_H3d zenon_H97 zenon_H21 zenon_H13f zenon_H23 zenon_H26 zenon_H16a zenon_H169 zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.74/5.91 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.74/5.91 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.74/5.91 apply (zenon_L605_); trivial. % 5.74/5.91 (* end of lemma zenon_L606_ *) % 5.74/5.91 assert (zenon_L607_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e2) = (e3))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((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 (e3) (e3)) = (e3))) -> False). % 5.74/5.91 do 0 intro. intros zenon_H16e zenon_H20 zenon_H14b zenon_H89 zenon_H6d zenon_Ha6 zenon_H123 zenon_Hb8 zenon_Hb7 zenon_Hcb zenon_H14f zenon_H150 zenon_H86 zenon_Hd9 zenon_H52 zenon_H25 zenon_H1d1 zenon_H63 zenon_H97 zenon_H21 zenon_H13f zenon_H23 zenon_H26 zenon_H16a zenon_H169 zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.74/5.91 exact (zenon_H20 zenon_H1f). % 5.74/5.91 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.74/5.91 apply (zenon_L512_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.74/5.91 apply (zenon_L594_); trivial. % 5.74/5.91 apply (zenon_L606_); trivial. % 5.74/5.91 (* end of lemma zenon_L607_ *) % 5.74/5.91 assert (zenon_L608_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((e1) = (e2))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e2)) = (e3)) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.74/5.91 do 0 intro. intros zenon_Hde zenon_H45 zenon_H105 zenon_Hed zenon_H95 zenon_H9a zenon_H97 zenon_H25 zenon_H1d1 zenon_Hd9 zenon_H1ad zenon_H86 zenon_H11f zenon_H22 zenon_H63 zenon_H16a zenon_H169 zenon_Hd3 zenon_H1a0 zenon_H52. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.91 apply (zenon_L16_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.91 apply (zenon_L76_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.91 apply (zenon_L58_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.91 apply (zenon_L449_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.91 apply (zenon_L34_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.91 apply (zenon_L9_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.91 apply (zenon_L59_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.91 apply (zenon_L508_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.91 apply (zenon_L190_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.91 apply (zenon_L61_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.91 apply (zenon_L62_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.91 apply (zenon_L310_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.91 apply (zenon_L510_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.91 apply (zenon_L281_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.91 apply (zenon_L63_); trivial. % 5.74/5.91 apply (zenon_L284_); trivial. % 5.74/5.91 (* end of lemma zenon_L608_ *) % 5.74/5.91 assert (zenon_L609_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((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 (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> ((op (e3) (e1)) = (e1)) -> False). % 5.74/5.91 do 0 intro. intros zenon_Hf6 zenon_H143 zenon_Had zenon_H150 zenon_H1cb zenon_H140 zenon_Hde zenon_H1a0 zenon_Hd3 zenon_H169 zenon_H86 zenon_H16a zenon_H1ad zenon_H11f zenon_H1d1 zenon_Hd9 zenon_H9a zenon_Hed zenon_H105 zenon_H95 zenon_H45 zenon_H20 zenon_H25 zenon_H24 zenon_H13f zenon_H21 zenon_H1e2 zenon_H52 zenon_H97 zenon_H63 zenon_H1e3 zenon_Hee zenon_Haf. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.74/5.91 exact (zenon_H20 zenon_H1f). % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.74/5.91 apply (zenon_L75_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.74/5.91 apply (zenon_L602_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H140); [ zenon_intro zenon_H22 | zenon_intro zenon_H141 ]. % 5.74/5.91 apply (zenon_L608_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H141); [ zenon_intro zenon_H28 | zenon_intro zenon_H142 ]. % 5.74/5.91 exact (zenon_H13f zenon_H28). % 5.74/5.91 apply (zenon_or_s _ _ zenon_H142); [ zenon_intro zenon_H12f | zenon_intro zenon_H124 ]. % 5.74/5.91 apply (zenon_L588_); trivial. % 5.74/5.91 apply (zenon_L265_); trivial. % 5.74/5.91 (* end of lemma zenon_L609_ *) % 5.74/5.91 assert (zenon_L610_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((e0) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e1)) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e1)) = (e0)) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.74/5.91 do 0 intro. intros zenon_Hde zenon_H113 zenon_H1c7 zenon_H72 zenon_H6d zenon_H9a zenon_H95 zenon_Hdc zenon_H59 zenon_H1e2 zenon_H97 zenon_H1e3 zenon_Hd9 zenon_H1ad zenon_H86 zenon_H11f zenon_H22 zenon_H63 zenon_H16a zenon_H169 zenon_Hca zenon_H143 zenon_H52. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.91 apply (zenon_L16_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.91 apply (zenon_L520_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.91 apply (zenon_L31_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.91 apply (zenon_L305_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.91 apply (zenon_L34_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.91 apply (zenon_L9_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.91 apply (zenon_L208_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.91 apply (zenon_L377_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.91 apply (zenon_L190_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.91 apply (zenon_L61_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.91 apply (zenon_L62_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.91 apply (zenon_L310_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.91 apply (zenon_L510_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.91 apply (zenon_L307_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.91 apply (zenon_L63_); trivial. % 5.74/5.91 apply (zenon_L284_); trivial. % 5.74/5.91 (* end of lemma zenon_L610_ *) % 5.74/5.91 assert (zenon_L611_ : (((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((e2) = (e3))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e0) (e2)) = (e0)) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e3))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e2)) = (e1))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e1) (e1)) = (e2))) -> ((op (e2) (e2)) = (e2)) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.74/5.91 do 0 intro. intros zenon_H3f zenon_Hf6 zenon_Hb7 zenon_Hb8 zenon_H171 zenon_H45 zenon_H63 zenon_H105 zenon_H86 zenon_H12a zenon_H110 zenon_H116 zenon_Hf0 zenon_H11f zenon_H33 zenon_H4a zenon_H113 zenon_H117 zenon_H97 zenon_Haa zenon_H26 zenon_H55 zenon_H57 zenon_H58 zenon_H59 zenon_H3e zenon_H154 zenon_Hf8 zenon_H77 zenon_H9d zenon_Hee zenon_H146 zenon_H1d1 zenon_H25 zenon_H52 zenon_Hd9 zenon_H1c7 zenon_H6d zenon_Hca. % 5.74/5.91 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.74/5.91 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.74/5.91 exact (zenon_H20 zenon_H1f). % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.74/5.91 exact (zenon_Hb8 zenon_Hba). % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.74/5.91 apply (zenon_L102_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.74/5.91 apply (zenon_L103_); trivial. % 5.74/5.91 apply (zenon_L537_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.74/5.91 apply (zenon_L333_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.74/5.91 apply (zenon_L108_); trivial. % 5.74/5.91 apply (zenon_L334_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.74/5.91 apply (zenon_L539_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.74/5.91 apply (zenon_L333_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.74/5.91 apply (zenon_L119_); trivial. % 5.74/5.91 apply (zenon_L334_); trivial. % 5.74/5.91 apply (zenon_L304_); trivial. % 5.74/5.91 (* end of lemma zenon_L611_ *) % 5.74/5.91 assert (zenon_L612_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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 (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (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 (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) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 5.74/5.91 do 0 intro. intros zenon_H195 zenon_H194 zenon_H188 zenon_H17d zenon_H174 zenon_H179 zenon_H16e zenon_H163 zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H14b zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf3 zenon_Hed zenon_Hdd zenon_Hdc zenon_Hce zenon_Ha7 zenon_H9f zenon_H117 zenon_H8f zenon_H4a zenon_H72 zenon_H8e zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H18a zenon_H32 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H23 zenon_H21 zenon_H52 zenon_H33 zenon_H154 zenon_H105 zenon_H55 zenon_Hb4 zenon_H171 zenon_H45 zenon_H41 zenon_H97 zenon_H63 zenon_Hb7 zenon_H86 zenon_H6d zenon_H9d zenon_Hb8 zenon_H169 zenon_H9a zenon_H11f zenon_Hd9 zenon_H1ad zenon_Hf6 zenon_H146 zenon_H57 zenon_Hf0 zenon_Hf8 zenon_H1d1 zenon_Haa zenon_H150 zenon_Hee zenon_H14f zenon_Hde zenon_H1ef zenon_H1a5 zenon_H1c7 zenon_H1e2 zenon_H1e3. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.91 apply (zenon_L16_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.91 apply (zenon_L3_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.91 apply (zenon_L58_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.91 apply (zenon_L573_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.91 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 5.74/5.91 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H20. % 5.74/5.91 apply (zenon_L593_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.91 apply (zenon_L9_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.91 apply (zenon_L59_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.91 apply (zenon_L332_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.91 apply (zenon_L190_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.91 apply (zenon_L61_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.91 apply (zenon_L62_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.91 apply (zenon_L310_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.91 apply (zenon_L575_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.91 apply (zenon_L447_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.91 apply (zenon_L63_); trivial. % 5.74/5.91 apply (zenon_L284_); trivial. % 5.74/5.91 apply (zenon_L263_); trivial. % 5.74/5.91 apply (zenon_L543_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.91 apply (zenon_L16_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.91 apply (zenon_L3_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.91 apply (zenon_L58_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.91 apply (zenon_L573_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.91 apply (zenon_L548_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.91 apply (zenon_L9_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.91 apply (zenon_L59_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.91 apply (zenon_L332_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.91 apply (zenon_L190_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.91 apply (zenon_L61_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.91 apply (zenon_L62_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.91 apply (zenon_L310_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.91 apply (zenon_L299_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.91 apply (zenon_L447_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.91 apply (zenon_L63_); trivial. % 5.74/5.91 apply (zenon_L284_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.91 apply (zenon_L16_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.91 apply (zenon_L3_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.91 apply (zenon_L58_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.91 apply (zenon_L305_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.91 apply (zenon_L611_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.91 apply (zenon_L9_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.91 apply (zenon_L106_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.91 apply (zenon_L377_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.91 apply (zenon_L109_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.91 apply (zenon_L61_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.91 apply (zenon_L62_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.91 apply (zenon_L310_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.91 apply (zenon_L574_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.91 apply (zenon_L307_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.91 apply (zenon_L63_); trivial. % 5.74/5.91 apply (zenon_L284_); trivial. % 5.74/5.91 apply (zenon_L72_); trivial. % 5.74/5.91 apply (zenon_L278_); trivial. % 5.74/5.91 apply (zenon_L298_); trivial. % 5.74/5.91 apply (zenon_L60_); trivial. % 5.74/5.91 apply (zenon_L33_); trivial. % 5.74/5.91 apply (zenon_L38_); trivial. % 5.74/5.91 (* end of lemma zenon_L612_ *) % 5.74/5.91 assert (zenon_L613_ : (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e0) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e0) (e2)) = (e0)) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e0) = (e1))) -> ((op (e2) (e0)) = (e0)) -> (~((e1) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.74/5.91 do 0 intro. intros zenon_H1cb zenon_H1e3 zenon_H1e2 zenon_H1c7 zenon_H1a5 zenon_H1ef zenon_Hde zenon_H14f zenon_H150 zenon_Haa zenon_H1d1 zenon_Hf8 zenon_Hf0 zenon_H57 zenon_H146 zenon_Hf6 zenon_H1ad zenon_Hd9 zenon_H11f zenon_H9a zenon_H169 zenon_Hb8 zenon_H6d zenon_H86 zenon_Hb7 zenon_H63 zenon_H97 zenon_H45 zenon_H171 zenon_Hb4 zenon_H55 zenon_H105 zenon_H154 zenon_H33 zenon_H52 zenon_H21 zenon_H23 zenon_H193 zenon_H191 zenon_H18c zenon_H18e zenon_H32 zenon_H18a zenon_H189 zenon_H185 zenon_H11e zenon_H11a zenon_H118 zenon_H100 zenon_Hfd zenon_H8e zenon_H72 zenon_H4a zenon_H8f zenon_H117 zenon_H9f zenon_Ha7 zenon_Hce zenon_Hdc zenon_Hdd zenon_Hed zenon_Hf3 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H14b zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H163 zenon_H16e zenon_H179 zenon_H174 zenon_H17d zenon_H188 zenon_H194 zenon_H195 zenon_Hee zenon_Hd6 zenon_H9d zenon_Hca. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.74/5.91 exact (zenon_H150 zenon_H152). % 5.74/5.91 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.74/5.91 apply (zenon_L612_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.74/5.91 apply (zenon_L121_); trivial. % 5.74/5.91 apply (zenon_L339_); trivial. % 5.74/5.91 (* end of lemma zenon_L613_ *) % 5.74/5.91 assert (zenon_L614_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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 (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (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 (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) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> False). % 5.74/5.91 do 0 intro. intros zenon_Hc8 zenon_H58 zenon_H59 zenon_H3e zenon_H25 zenon_H9d zenon_Hee zenon_H195 zenon_H194 zenon_H188 zenon_H17d zenon_H174 zenon_H179 zenon_H16e zenon_H163 zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H14b zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf3 zenon_Hed zenon_Hdd zenon_Hdc zenon_Hce zenon_Ha7 zenon_H9f zenon_H117 zenon_H8f zenon_H4a zenon_H72 zenon_H8e zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H18a zenon_H32 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H23 zenon_H21 zenon_H52 zenon_H33 zenon_H154 zenon_H105 zenon_H55 zenon_Hb4 zenon_H171 zenon_H45 zenon_H97 zenon_H63 zenon_Hb7 zenon_H86 zenon_Hb8 zenon_H169 zenon_H9a zenon_H11f zenon_Hd9 zenon_H1ad zenon_Hf6 zenon_H146 zenon_H57 zenon_Hf0 zenon_Hf8 zenon_H1d1 zenon_Haa zenon_H150 zenon_H14f zenon_Hde zenon_H1ef zenon_H1a5 zenon_H1c7 zenon_H1e2 zenon_H1e3 zenon_H1cb zenon_H6d. % 5.74/5.91 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.91 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.74/5.91 exact (zenon_H20 zenon_H1f). % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.74/5.91 apply (zenon_L538_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.74/5.91 apply (zenon_L613_); trivial. % 5.74/5.91 apply (zenon_L304_); trivial. % 5.74/5.91 (* end of lemma zenon_L614_ *) % 5.74/5.91 assert (zenon_L615_ : (((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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 (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (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 (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) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> False). % 5.74/5.91 do 0 intro. intros zenon_Hc8 zenon_H58 zenon_H59 zenon_H3e zenon_H25 zenon_H9d zenon_Hee zenon_H195 zenon_H194 zenon_H188 zenon_H17d zenon_H174 zenon_H179 zenon_H16e zenon_H163 zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H14b zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf3 zenon_Hed zenon_Hdd zenon_Hdc zenon_Hce zenon_Ha7 zenon_H9f zenon_H117 zenon_H8f zenon_H4a zenon_H72 zenon_H8e zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H18a zenon_H32 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H23 zenon_H21 zenon_H52 zenon_H33 zenon_H154 zenon_H105 zenon_H55 zenon_Hb4 zenon_H171 zenon_H45 zenon_H97 zenon_H63 zenon_Hb7 zenon_H86 zenon_Hb8 zenon_H169 zenon_H9a zenon_H11f zenon_Hd9 zenon_H1ad zenon_Hf6 zenon_H146 zenon_H57 zenon_Hf0 zenon_Hf8 zenon_H1d1 zenon_Haa zenon_H150 zenon_H14f zenon_Hde zenon_H1ef zenon_H1a5 zenon_H1c7 zenon_H1e2 zenon_H1e3 zenon_H1cb zenon_H6d. % 5.74/5.91 apply (zenon_L614_); trivial. % 5.74/5.91 (* end of lemma zenon_L615_ *) % 5.74/5.91 assert (zenon_L616_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e0) = (e2))) -> False). % 5.74/5.91 do 0 intro. intros zenon_H3b zenon_H169 zenon_H16a zenon_H143 zenon_H1c2 zenon_Hee zenon_H1e3 zenon_H97 zenon_H1e2 zenon_H21 zenon_H13f zenon_H24 zenon_H25 zenon_H140 zenon_H11f zenon_H52 zenon_H63. % 5.74/5.91 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.74/5.91 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.74/5.91 apply (zenon_L589_); trivial. % 5.74/5.91 (* end of lemma zenon_L616_ *) % 5.74/5.91 assert (zenon_L617_ : ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((e0) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((e1) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e2))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (((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) (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)) = (e0))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e0) = (e3))) -> ((op (e0) (e3)) = (e0)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.74/5.91 do 0 intro. intros zenon_Hde zenon_Hdc zenon_H63 zenon_H140 zenon_H25 zenon_H24 zenon_H13f zenon_H21 zenon_H1e2 zenon_H97 zenon_H1e3 zenon_Hee zenon_H1c2 zenon_H143 zenon_H16a zenon_H169 zenon_H1cb zenon_H150 zenon_H9a zenon_H105 zenon_H45 zenon_H20 zenon_Hf6 zenon_H11f zenon_Hd9 zenon_H1ad zenon_H6d zenon_H3d zenon_H9d zenon_H95 zenon_H52. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.91 apply (zenon_L16_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.91 apply (zenon_L76_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.91 apply (zenon_L58_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.91 apply (zenon_L616_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.91 apply (zenon_L34_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.91 apply (zenon_L9_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.91 apply (zenon_L208_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.91 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.74/5.91 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.74/5.91 apply (zenon_L603_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.91 apply (zenon_L190_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.91 apply (zenon_L61_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.91 apply (zenon_L62_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.91 apply (zenon_L310_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.91 apply (zenon_L484_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.91 apply (zenon_L346_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.91 apply (zenon_L63_); trivial. % 5.74/5.91 apply (zenon_L284_); trivial. % 5.74/5.91 (* end of lemma zenon_L617_ *) % 5.74/5.91 assert (zenon_L618_ : (~((e0) = (e3))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (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)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e3)) = (e1))) -> (~((op (e3) (e3)) = (e2))) -> (~((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (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 (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) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((op (e3) (e0)) = (e3)) -> (~((e1) = (e3))) -> ((op (e1) (e3)) = (e1)) -> ((op (e2) (e2)) = (e2)) -> False). % 5.74/5.91 do 0 intro. intros zenon_H6d zenon_H1ad zenon_Hd9 zenon_H11f zenon_Hf6 zenon_H20 zenon_H45 zenon_H105 zenon_H9a zenon_H150 zenon_H1cb zenon_H169 zenon_H16a zenon_H143 zenon_H1c2 zenon_Hee zenon_H1e3 zenon_H97 zenon_H1e2 zenon_H21 zenon_H13f zenon_H24 zenon_H25 zenon_H140 zenon_H63 zenon_Hdc zenon_Hde zenon_H58 zenon_H59 zenon_H3e zenon_H195 zenon_H194 zenon_H188 zenon_H17d zenon_H174 zenon_H179 zenon_H16e zenon_H163 zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H14b zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf3 zenon_Hed zenon_Hdd zenon_Hce zenon_Ha7 zenon_H9f zenon_H117 zenon_H8f zenon_H4a zenon_H72 zenon_H8e zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H18a zenon_H32 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H23 zenon_H154 zenon_H55 zenon_Hb4 zenon_H171 zenon_Hb7 zenon_H86 zenon_Hb8 zenon_H146 zenon_H57 zenon_Hf0 zenon_Hf8 zenon_H1d1 zenon_Haa zenon_H14f zenon_H1ef zenon_H1a5 zenon_H1c7 zenon_Hca zenon_H9d zenon_H95 zenon_H52. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.91 apply (zenon_L16_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.91 apply (zenon_L76_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.91 apply (zenon_L58_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.91 apply (zenon_L305_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.91 apply (zenon_L34_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.91 apply (zenon_L9_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.91 apply (zenon_L208_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.91 apply (zenon_L377_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.91 apply (zenon_L190_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.91 apply (zenon_L61_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.91 apply (zenon_L62_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.91 apply (zenon_L310_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.74/5.91 exact (zenon_H20 zenon_H1f). % 5.74/5.91 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.74/5.91 apply (zenon_L610_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.74/5.91 apply (zenon_L615_); trivial. % 5.74/5.91 apply (zenon_L617_); trivial. % 5.74/5.91 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.92 apply (zenon_L346_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.92 apply (zenon_L63_); trivial. % 5.74/5.92 apply (zenon_L284_); trivial. % 5.74/5.92 (* end of lemma zenon_L618_ *) % 5.74/5.92 assert (zenon_L619_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e0) (e0)) = (e1))) -> (((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 (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e1)) = (op (e3) (e2)))) -> ((op (e3) (e2)) = (e3)) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (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)) = (e0))) -> (~((op (e1) (e1)) = (e2))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e0) = (e1))) -> False). % 5.74/5.92 do 0 intro. intros zenon_Hf6 zenon_H143 zenon_Had zenon_H150 zenon_H1cb zenon_H140 zenon_Hde zenon_H1a0 zenon_Hd3 zenon_H169 zenon_H86 zenon_H16a zenon_H1ad zenon_H11f zenon_H1d1 zenon_Hd9 zenon_H9a zenon_Hed zenon_H105 zenon_H45 zenon_H20 zenon_H25 zenon_H24 zenon_H13f zenon_H21 zenon_H1e2 zenon_H52 zenon_H97 zenon_H63 zenon_H1e3 zenon_Hee. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.74/5.92 apply (zenon_L609_); trivial. % 5.74/5.92 (* end of lemma zenon_L619_ *) % 5.74/5.92 assert (zenon_L620_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((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). % 5.74/5.92 do 0 intro. intros zenon_H14f zenon_H150 zenon_H63 zenon_H52 zenon_H11f zenon_H97 zenon_H16a zenon_H169 zenon_H1a6 zenon_H46 zenon_H3d zenon_Hee. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.74/5.92 exact (zenon_H150 zenon_H152). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.74/5.92 apply (zenon_L188_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.74/5.92 apply (zenon_L290_); trivial. % 5.74/5.92 apply (zenon_L161_); trivial. % 5.74/5.92 (* end of lemma zenon_L620_ *) % 5.74/5.92 assert (zenon_L621_ : (((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((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)) -> (~((e0) = (e1))) -> False). % 5.74/5.92 do 0 intro. intros zenon_H3b zenon_H14f zenon_H150 zenon_H63 zenon_H52 zenon_H11f zenon_H97 zenon_H16a zenon_H169 zenon_H1a6 zenon_H46 zenon_Hee. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.74/5.92 apply (zenon_L620_); trivial. % 5.74/5.92 (* end of lemma zenon_L621_ *) % 5.74/5.92 assert (zenon_L622_ : ((op (e0) (e3)) = (e3)) -> ((op (e1) (e2)) = (e1)) -> (~((op (e1) (e1)) = (e3))) -> (~((e1) = (e3))) -> (~((e0) = (e1))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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 (e1) (e2)) = (op (e2) (e2)))) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (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 (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) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (~((e0) = (e3))) -> ((op (e3) (e0)) = (e3)) -> False). % 5.74/5.92 do 0 intro. intros zenon_Hb3 zenon_H46 zenon_H26 zenon_H9d zenon_Hee zenon_H195 zenon_H194 zenon_H188 zenon_H17d zenon_H174 zenon_H179 zenon_H16e zenon_H163 zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H14b zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf3 zenon_Hed zenon_Hdd zenon_Hdc zenon_Hce zenon_Ha7 zenon_H9f zenon_H117 zenon_H8f zenon_H4a zenon_H72 zenon_H8e zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H18a zenon_H32 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H20 zenon_H23 zenon_H21 zenon_H52 zenon_H33 zenon_H154 zenon_H105 zenon_H55 zenon_Hb4 zenon_H171 zenon_H45 zenon_H97 zenon_H63 zenon_Hb7 zenon_H86 zenon_Hb8 zenon_H169 zenon_H9a zenon_H11f zenon_Hd9 zenon_H1ad zenon_Hf6 zenon_H146 zenon_H57 zenon_Hf0 zenon_Hf8 zenon_H1d1 zenon_Haa zenon_H150 zenon_H14f zenon_Hde zenon_H1ef zenon_H1a5 zenon_H1c7 zenon_H1e2 zenon_H1e3 zenon_H1cb zenon_H6d zenon_Hca. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.74/5.92 exact (zenon_H20 zenon_H1f). % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H8e); [ zenon_intro zenon_H6c | zenon_intro zenon_H90 ]. % 5.74/5.92 apply (zenon_L19_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H2d | zenon_intro zenon_H91 ]. % 5.74/5.92 exact (zenon_H26 zenon_H2d). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H85 | zenon_intro zenon_H89 ]. % 5.74/5.92 apply (zenon_L35_); trivial. % 5.74/5.92 apply (zenon_L392_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.74/5.92 apply (zenon_L613_); trivial. % 5.74/5.92 apply (zenon_L304_); trivial. % 5.74/5.92 (* end of lemma zenon_L622_ *) % 5.74/5.92 assert (zenon_L623_ : (~((op (e3) (e3)) = (e2))) -> (~((op (e0) (e0)) = (e2))) -> ((op (e3) (e0)) = (e3)) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (((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 (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e3)))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e3))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e0) = (e2))) -> (~((e1) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (((op (e0) (e3)) = (e1))\/(((op (e1) (e3)) = (e1))\/(((op (e2) (e3)) = (e1))\/((op (e3) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> ((op (e2) (e2)) = (e2)) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> (((op (e1) (e0)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e2)) = (e1))\/((op (e1) (e3)) = (e1))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((e0) = (e1))) -> (~((e1) = (e3))) -> (~((op (e1) (e1)) = (e3))) -> ((op (e1) (e2)) = (e1)) -> ((op (e0) (e3)) = (e3)) -> (~((e0) = (e3))) -> False). % 5.74/5.92 do 0 intro. intros zenon_H59 zenon_H16a zenon_Hca zenon_H1cb zenon_H1e3 zenon_H1e2 zenon_H1c7 zenon_H1a5 zenon_H1ef zenon_Hde zenon_H14f zenon_H150 zenon_Haa zenon_H1d1 zenon_Hf8 zenon_Hf0 zenon_H57 zenon_H146 zenon_Hf6 zenon_H1ad zenon_Hd9 zenon_H11f zenon_H9a zenon_H169 zenon_Hb8 zenon_H86 zenon_Hb7 zenon_H63 zenon_H97 zenon_H45 zenon_H171 zenon_Hb4 zenon_H55 zenon_H105 zenon_H154 zenon_H52 zenon_H21 zenon_H23 zenon_H20 zenon_H193 zenon_H191 zenon_H18c zenon_H18e zenon_H32 zenon_H18a zenon_H189 zenon_H185 zenon_H11e zenon_H11a zenon_H118 zenon_H100 zenon_Hfd zenon_H8e zenon_H72 zenon_H4a zenon_H8f zenon_H117 zenon_H9f zenon_Ha7 zenon_Hce zenon_Hdc zenon_Hdd zenon_Hed zenon_Hf3 zenon_H116 zenon_H113 zenon_H110 zenon_H10d zenon_H10a zenon_H115 zenon_H114 zenon_H11d zenon_H158 zenon_H155 zenon_H14b zenon_H140 zenon_H143 zenon_H126 zenon_H123 zenon_H122 zenon_H129 zenon_H12a zenon_H163 zenon_H16e zenon_H179 zenon_H174 zenon_H17d zenon_H188 zenon_H194 zenon_H195 zenon_Hee zenon_H9d zenon_H26 zenon_H46 zenon_Hb3 zenon_H6d. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.74/5.92 exact (zenon_H20 zenon_H1f). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.74/5.92 apply (zenon_L522_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.74/5.92 apply (zenon_L622_); trivial. % 5.74/5.92 apply (zenon_L271_); trivial. % 5.74/5.92 (* end of lemma zenon_L623_ *) % 5.74/5.92 assert (zenon_L624_ : (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((e0) = (e2))) -> ((op (e0) (e3)) = (e0)) -> ((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 (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 (e3) (e3)) = (e3))) -> False). % 5.74/5.92 do 0 intro. intros zenon_H14f zenon_H150 zenon_H63 zenon_H3d zenon_H52 zenon_H11f zenon_H97 zenon_H16a zenon_H169 zenon_H1a6 zenon_H46 zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.74/5.92 exact (zenon_H150 zenon_H152). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.74/5.92 apply (zenon_L188_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.74/5.92 apply (zenon_L290_); trivial. % 5.74/5.92 apply (zenon_L292_); trivial. % 5.74/5.92 (* end of lemma zenon_L624_ *) % 5.74/5.92 assert (zenon_L625_ : (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((e2) = (e3))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (~((op (e0) (e0)) = (e0))) -> (~((e1) = (e3))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e2) (e2)) = (e0))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e1) (e3)) = (e3)) -> (~((e0) = (e3))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((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 (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 (e3) (e3)) = (e3))) -> False). % 5.74/5.92 do 0 intro. intros zenon_H16e zenon_Hee zenon_H13f zenon_H122 zenon_H17d zenon_H10a zenon_H1a5 zenon_Hf3 zenon_Hde zenon_H143 zenon_H1ad zenon_H1e3 zenon_H1e2 zenon_H24 zenon_H9f zenon_H72 zenon_H1c7 zenon_H86 zenon_H113 zenon_H20 zenon_H9d zenon_H105 zenon_H4b zenon_H18e zenon_H1c2 zenon_Hf6 zenon_H14b zenon_H89 zenon_H6d zenon_Ha6 zenon_H123 zenon_Hb8 zenon_Hb7 zenon_H14f zenon_H150 zenon_H63 zenon_H52 zenon_H11f zenon_H97 zenon_H16a zenon_H169 zenon_H1a6 zenon_H46 zenon_H55 zenon_Hf7 zenon_Hb4 zenon_H59 zenon_H3e. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H16e); [ zenon_intro zenon_H1f | zenon_intro zenon_H16f ]. % 5.74/5.92 exact (zenon_H20 zenon_H1f). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H16f); [ zenon_intro zenon_H22 | zenon_intro zenon_H170 ]. % 5.74/5.92 apply (zenon_L525_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H170); [ zenon_intro zenon_H33 | zenon_intro zenon_H3d ]. % 5.74/5.92 apply (zenon_L594_); trivial. % 5.74/5.92 apply (zenon_L624_); trivial. % 5.74/5.92 (* end of lemma zenon_L625_ *) % 5.74/5.92 assert (zenon_L626_ : (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e0) (e0)) = (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) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e1) (e0)) = (e1))\/(((op (e2) (e0)) = (e1))\/((op (e3) (e0)) = (e1))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((e0) = (e1))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> (~((e1) = (e2))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e1) (e1)) = (e0))) -> (~((op (e1) (e1)) = (e1))) -> (~((op (e1) (e1)) = (e2))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((op (e3) (e1)) = (e0))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e3)) = (e0)) -> (~((e0) = (e2))) -> False). % 5.74/5.92 do 0 intro. intros zenon_Hf6 zenon_H20 zenon_H45 zenon_H105 zenon_Had zenon_H9a zenon_H150 zenon_H1cb zenon_H169 zenon_H16a zenon_H143 zenon_H1c2 zenon_Hee zenon_H1e3 zenon_H97 zenon_H1e2 zenon_H21 zenon_H13f zenon_H24 zenon_H25 zenon_H140 zenon_H11f zenon_H52 zenon_H3d zenon_H63. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.74/5.92 apply (zenon_L603_); trivial. % 5.74/5.92 (* end of lemma zenon_L626_ *) % 5.74/5.92 assert (zenon_L627_ : ((op (e0) (e3)) = (e0)) -> ((op (e1) (e0)) = (e1)) -> (~((op (e0) (e0)) = (e2))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((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)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((e0) = (e1))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> (~((e0) = (e2))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> ((op (e2) (e2)) = (e2)) -> (~((e1) = (e2))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (~((e2) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e0) (e0)) = (e0))) -> False). % 5.74/5.92 do 0 intro. intros zenon_H3d zenon_H41 zenon_H16a zenon_H122 zenon_H17d zenon_H1a5 zenon_H143 zenon_H1e3 zenon_H1e2 zenon_H1c2 zenon_H18e zenon_H1c7 zenon_H55 zenon_H21 zenon_H23 zenon_H195 zenon_H100 zenon_H8e zenon_H57 zenon_H8f zenon_H6d zenon_H9d zenon_H9f zenon_Ha7 zenon_Haa zenon_Hb4 zenon_Hb7 zenon_Hce zenon_Hdd zenon_Hf8 zenon_Hee zenon_Hf3 zenon_Hf6 zenon_H113 zenon_H10a zenon_H115 zenon_H114 zenon_H63 zenon_H45 zenon_H52 zenon_H97 zenon_H105 zenon_H72 zenon_Hed zenon_H9a zenon_Hdc zenon_Hd9 zenon_H1d1 zenon_H11f zenon_H1ad zenon_H86 zenon_H169 zenon_Hde zenon_H158 zenon_H11d zenon_H11e zenon_H189 zenon_H118 zenon_H188 zenon_H20. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.92 apply (zenon_L16_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.92 apply (zenon_L532_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.92 apply (zenon_L58_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.92 apply (zenon_L591_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.92 apply (zenon_L200_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.92 apply (zenon_L9_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.92 apply (zenon_L59_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.92 apply (zenon_L332_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.92 apply (zenon_L190_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.92 apply (zenon_L61_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.92 apply (zenon_L62_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.92 apply (zenon_L310_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.92 apply (zenon_L484_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.92 apply (zenon_L447_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.92 apply (zenon_L63_); trivial. % 5.74/5.92 apply (zenon_L284_); trivial. % 5.74/5.92 apply (zenon_L38_); trivial. % 5.74/5.92 (* end of lemma zenon_L627_ *) % 5.74/5.92 assert (zenon_L628_ : (((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1))))) -> (((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)))) -> (~((e0) = (e3))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.74/5.92 do 0 intro. intros zenon_Hcb zenon_Hb7 zenon_Hb8 zenon_H123 zenon_H6d zenon_H33 zenon_H14b. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.74/5.92 apply (zenon_L594_); trivial. % 5.74/5.92 (* end of lemma zenon_L628_ *) % 5.74/5.92 assert (zenon_L629_ : (~((op (e1) (e1)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (~((op (e1) (e2)) = (op (e2) (e2)))) -> (~((e0) = (e2))) -> (~((op (e0) (e0)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((e0) = (e1))) -> (((op (e0) (e3)) = (e0))\/(((op (e1) (e3)) = (e0))\/(((op (e2) (e3)) = (e0))\/((op (e3) (e3)) = (e0))))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e0) (e3)) = (op (e3) (e3)))) -> (((op (e0) (e1)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e2) (e1)) = (e3))\/((op (e3) (e1)) = (e3))))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (~((op (e1) (e3)) = (op (e3) (e3)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (((op (e0) (e1)) = (e1))\/(((op (e1) (e1)) = (e1))\/(((op (e2) (e1)) = (e1))\/((op (e3) (e1)) = (e1))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (~((e2) = (e3))) -> (~((op (e1) (e1)) = (e2))) -> (~((e1) = (e2))) -> (((op (e0) (e1)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e2) (e1)) = (e2))\/((op (e3) (e1)) = (e2))))) -> (~((e1) = (e3))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> ((op (e3) (e1)) = (e3)) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> ((op (e0) (e2)) = (e0)) -> (~((e0) = (e3))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> False). % 5.74/5.92 do 0 intro. intros zenon_H188 zenon_H118 zenon_H189 zenon_H11e zenon_H11d zenon_H158 zenon_Hde zenon_H169 zenon_Hdc zenon_H9a zenon_Hed zenon_H72 zenon_H105 zenon_H45 zenon_H63 zenon_H20 zenon_H114 zenon_H115 zenon_H10a zenon_H113 zenon_Hf6 zenon_Hf3 zenon_Hee zenon_Hf8 zenon_Hdd zenon_Hce zenon_Hb4 zenon_Haa zenon_Ha7 zenon_H9f zenon_H8f zenon_H57 zenon_H8e zenon_H100 zenon_H195 zenon_H23 zenon_H21 zenon_H55 zenon_H1c7 zenon_H18e zenon_H1c2 zenon_H1e2 zenon_H1e3 zenon_H1a5 zenon_H17d zenon_H122 zenon_H154 zenon_H86 zenon_H25 zenon_H97 zenon_H1d1 zenon_H9d zenon_H11f zenon_Hd9 zenon_H1ad zenon_Ha6 zenon_H143 zenon_H14b zenon_H33 zenon_H6d zenon_H123 zenon_Hb8 zenon_Hb7 zenon_H52. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.92 apply (zenon_L16_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.92 apply (zenon_L532_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.92 apply (zenon_L58_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.92 apply (zenon_L573_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.92 apply (zenon_L548_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.92 apply (zenon_L9_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.92 apply (zenon_L59_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.92 apply (zenon_L295_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.92 apply (zenon_L190_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.92 apply (zenon_L61_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.92 apply (zenon_L62_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.92 apply (zenon_L310_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.92 apply (zenon_L299_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.92 apply (zenon_L628_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.92 apply (zenon_L63_); trivial. % 5.74/5.92 apply (zenon_L284_); trivial. % 5.74/5.92 (* end of lemma zenon_L629_ *) % 5.74/5.92 assert (zenon_L630_ : (((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3))))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> (~((op (e0) (e0)) = (e1))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (~((e0) = (e1))) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e3)) = (op (e1) (e3)))) -> False). % 5.74/5.92 do 0 intro. intros zenon_Had zenon_H14f zenon_H150 zenon_H123 zenon_Hee zenon_H33 zenon_H14b. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.74/5.92 apply (zenon_L556_); trivial. % 5.74/5.92 (* end of lemma zenon_L630_ *) % 5.74/5.92 assert (zenon_L631_ : ((~((op (e3) (e3)) = (e3)))\/((op (e3) (e3)) = (e3))) -> ((~((op (e0) (e0)) = (e1)))\/((op (e0) (e1)) = (e0))) -> (~((op (e1) (e1)) = (op (e1) (e3)))) -> (((op (e1) (e0)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e1) (e2)) = (e0))\/((op (e1) (e3)) = (e0))))) -> (~((op (e0) (e3)) = (op (e2) (e3)))) -> ((~((op (e3) (e3)) = (e1)))\/((op (e3) (e1)) = (e3))) -> (((op (e0) (e0)) = (e0))\/(((op (e0) (e1)) = (e0))\/(((op (e0) (e2)) = (e0))\/((op (e0) (e3)) = (e0))))) -> (((op (e0) (e2)) = (e1))\/(((op (e1) (e2)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e3) (e2)) = (e1))))) -> ((~((op (e2) (e2)) = (e1)))\/((op (e2) (e1)) = (e2))) -> (~((op (e2) (e1)) = (op (e2) (e3)))) -> (~((op (e1) (e0)) = (op (e3) (e0)))) -> (~((op (e0) (e1)) = (op (e3) (e1)))) -> (((op (e3) (e0)) = (e0))\/(((op (e3) (e1)) = (e0))\/(((op (e3) (e2)) = (e0))\/((op (e3) (e3)) = (e0))))) -> (~((op (e3) (e0)) = (op (e3) (e1)))) -> (((op (e0) (e1)) = (e0))\/(((op (e1) (e1)) = (e0))\/(((op (e2) (e1)) = (e0))\/((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 (e1) (e1)) = (e0)))\/((op (e1) (e0)) = (e1))) -> ((~((op (e0) (e0)) = (e3)))\/((op (e0) (e3)) = (e0))) -> ((~((op (e1) (e1)) = (e2)))\/((op (e1) (e2)) = (e1))) -> ((~((op (e2) (e2)) = (e0)))\/((op (e2) (e0)) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e1) (e0)) = (e3))\/(((op (e2) (e0)) = (e3))\/((op (e3) (e0)) = (e3))))) -> (((op (e2) (e0)) = (e3))\/(((op (e2) (e1)) = (e3))\/(((op (e2) (e2)) = (e3))\/((op (e2) (e3)) = (e3))))) -> (~((op (e2) (e0)) = (op (e2) (e1)))) -> (~((op (e2) (e0)) = (op (e2) (e2)))) -> ((~((op (e2) (e2)) = (e3)))\/((op (e2) (e3)) = (e2))) -> (~((op (e3) (e0)) = (op (e3) (e2)))) -> (~((op (e0) (e1)) = (op (e0) (e3)))) -> ((~((op (e1) (e1)) = (e3)))\/((op (e1) (e3)) = (e1))) -> (~((op (e1) (e2)) = (op (e1) (e3)))) -> (~((op (e2) (e3)) = (op (e3) (e3)))) -> (~((op (e3) (e1)) = (op (e3) (e3)))) -> (~((op (e1) (e0)) = (op (e1) (e2)))) -> ((~((op (e2) (e2)) = (e2)))\/((op (e2) (e2)) = (e2))) -> (((op (e0) (e2)) = (e0))\/(((op (e1) (e2)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e3) (e2)) = (e0))))) -> (((op (e2) (e2)) = (e0))\/(((op (e2) (e2)) = (e1))\/(((op (e2) (e2)) = (e2))\/((op (e2) (e2)) = (e3))))) -> (~((op (e0) (e1)) = (op (e0) (e2)))) -> (((op (e1) (e0)) = (e3))\/(((op (e1) (e1)) = (e3))\/(((op (e1) (e2)) = (e3))\/((op (e1) (e3)) = (e3))))) -> (~((op (e3) (e0)) = (op (e3) (e3)))) -> ((~((op (e3) (e3)) = (e0)))\/((op (e3) (e0)) = (e3))) -> (~((op (e1) (e0)) = (op (e1) (e1)))) -> (~((op (e1) (e1)) = (op (e2) (e1)))) -> ((~((op (e1) (e1)) = (e1)))\/((op (e1) (e1)) = (e1))) -> (((op (e3) (e0)) = (e1))\/(((op (e3) (e1)) = (e1))\/(((op (e3) (e2)) = (e1))\/((op (e3) (e3)) = (e1))))) -> ((~((op (e0) (e0)) = (e2)))\/((op (e0) (e2)) = (e0))) -> (~((op (e0) (e0)) = (op (e0) (e1)))) -> (~((op (e0) (e0)) = (op (e0) (e2)))) -> (((op (e2) (e0)) = (e0))\/(((op (e2) (e1)) = (e0))\/(((op (e2) (e2)) = (e0))\/((op (e2) (e3)) = (e0))))) -> (~((op (e0) (e0)) = (op (e2) (e0)))) -> (~((op (e0) (e0)) = (op (e1) (e0)))) -> ((~((op (e0) (e0)) = (e0)))\/((op (e0) (e0)) = (e0))) -> (~((op (e0) (e1)) = (op (e1) (e1)))) -> (((op (e1) (e1)) = (e0))\/(((op (e1) (e1)) = (e1))\/(((op (e1) (e1)) = (e2))\/((op (e1) (e1)) = (e3))))) -> ((op (e2) (e2)) = (e2)) -> ((op (e0) (e2)) = (e0)) -> (~((op (e0) (e2)) = (op (e0) (e3)))) -> (((op (e1) (e0)) = (e2))\/(((op (e1) (e1)) = (e2))\/(((op (e1) (e2)) = (e2))\/((op (e1) (e3)) = (e2))))) -> (((op (e3) (e3)) = (e0))\/(((op (e3) (e3)) = (e1))\/(((op (e3) (e3)) = (e2))\/((op (e3) (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 (e1) (e2)) = (op (e2) (e2)))) -> ((op (e1) (e0)) = (e1)) -> (~((e1) = (e2))) -> (~((e0) = (e2))) -> (((op (e0) (e0)) = (e3))\/(((op (e0) (e1)) = (e3))\/(((op (e0) (e2)) = (e3))\/((op (e0) (e3)) = (e3))))) -> (~((e2) = (e3))) -> (~((e0) = (e3))) -> (~((e1) = (e3))) -> (~((op (e0) (e0)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e0) (e1)) = (e2))\/(((op (e0) (e2)) = (e2))\/((op (e0) (e3)) = (e2))))) -> (~((op (e1) (e0)) = (op (e1) (e3)))) -> (~((op (e0) (e2)) = (op (e2) (e2)))) -> (~((op (e2) (e1)) = (op (e2) (e2)))) -> (~((op (e2) (e2)) = (op (e2) (e3)))) -> (((op (e0) (e0)) = (e0))\/(((op (e1) (e0)) = (e0))\/(((op (e2) (e0)) = (e0))\/((op (e3) (e0)) = (e0))))) -> (((op (e2) (e0)) = (e1))\/(((op (e2) (e1)) = (e1))\/(((op (e2) (e2)) = (e1))\/((op (e2) (e3)) = (e1))))) -> (~((op (e1) (e3)) = (op (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 (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) (e0)) = (e1))) -> (~((e0) = (e1))) -> (((op (e0) (e0)) = (e1))\/(((op (e0) (e1)) = (e1))\/(((op (e0) (e2)) = (e1))\/((op (e0) (e3)) = (e1))))) -> ((((op (e0) (e0)) = (e0))/\(((op (e0) (e0)) = (e0))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e0) (e1)) = (e0))/\(((op (e1) (e0)) = (e0))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e0) (e2)) = (e0))/\(((op (e2) (e0)) = (e0))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e0) (e3)) = (e0))/\(((op (e3) (e0)) = (e0))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e1) (e0)) = (e1))/\(((op (e0) (e1)) = (e1))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e1) (e1)) = (e1))/\(((op (e1) (e1)) = (e1))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e1) (e2)) = (e1))/\(((op (e2) (e1)) = (e1))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e1) (e3)) = (e1))/\(((op (e3) (e1)) = (e1))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e2) (e0)) = (e2))/\(((op (e0) (e2)) = (e2))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e2) (e1)) = (e2))/\(((op (e1) (e2)) = (e2))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e2) (e2)) = (e2))/\(((op (e2) (e2)) = (e2))/\(~((op (e2) (e2)) = (e2)))))\/((((op (e2) (e3)) = (e2))/\(((op (e3) (e2)) = (e2))/\(~((op (e3) (e3)) = (e3)))))\/((((op (e3) (e0)) = (e3))/\(((op (e0) (e3)) = (e3))/\(~((op (e0) (e0)) = (e0)))))\/((((op (e3) (e1)) = (e3))/\(((op (e1) (e3)) = (e3))/\(~((op (e1) (e1)) = (e1)))))\/((((op (e3) (e2)) = (e3))/\(((op (e2) (e3)) = (e3))/\(~((op (e2) (e2)) = (e2)))))\/(((op (e3) (e3)) = (e3))/\(((op (e3) (e3)) = (e3))/\(~((op (e3) (e3)) = (e3)))))))))))))))))))) -> (~((op (e1) (e2)) = (op (e3) (e2)))) -> ((~((op (e3) (e3)) = (e2)))\/((op (e3) (e2)) = (e3))) -> (((op (e0) (e0)) = (e2))\/(((op (e1) (e0)) = (e2))\/(((op (e2) (e0)) = (e2))\/((op (e3) (e0)) = (e2))))) -> (~((op (e2) (e2)) = (op (e3) (e2)))) -> (((op (e3) (e0)) = (e2))\/(((op (e3) (e1)) = (e2))\/(((op (e3) (e2)) = (e2))\/((op (e3) (e3)) = (e2))))) -> False). % 5.74/5.92 do 0 intro. intros zenon_H195 zenon_H194 zenon_H188 zenon_H17d zenon_H174 zenon_H179 zenon_H16e zenon_H163 zenon_H12a zenon_H129 zenon_H122 zenon_H123 zenon_H126 zenon_H143 zenon_H140 zenon_H14b zenon_H155 zenon_H158 zenon_H11d zenon_H114 zenon_H115 zenon_H10a zenon_H10d zenon_H110 zenon_H113 zenon_H116 zenon_Hf3 zenon_Hed zenon_Hdd zenon_Hdc zenon_Hce zenon_Ha7 zenon_H9f zenon_H117 zenon_H8f zenon_H4a zenon_H72 zenon_H8e zenon_Hfd zenon_H100 zenon_H118 zenon_H11a zenon_H11e zenon_H185 zenon_H189 zenon_H18a zenon_H32 zenon_H18e zenon_H18c zenon_H191 zenon_H193 zenon_H23 zenon_H21 zenon_H52 zenon_H33 zenon_H154 zenon_H105 zenon_H55 zenon_Hb4 zenon_H171 zenon_H45 zenon_H41 zenon_H97 zenon_H63 zenon_Hb7 zenon_H86 zenon_H6d zenon_H9d zenon_Hb8 zenon_H169 zenon_H9a zenon_H11f zenon_Hd9 zenon_H1ad zenon_Hf6 zenon_H146 zenon_H57 zenon_Hf0 zenon_Hf8 zenon_H1d1 zenon_Haa zenon_H150 zenon_Hee zenon_H14f zenon_Hde zenon_H1ef zenon_H1a5 zenon_H1c7 zenon_H1e2 zenon_H1e3. % 5.74/5.92 apply (zenon_L612_); trivial. % 5.74/5.92 (* end of lemma zenon_L631_ *) % 5.74/5.92 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H21e. zenon_intro zenon_H21d. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H220. zenon_intro zenon_H21f. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H21f). zenon_intro zenon_H222. zenon_intro zenon_H221. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H221). zenon_intro zenon_H224. zenon_intro zenon_H223. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H226. zenon_intro zenon_H225. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H225). zenon_intro zenon_H21. zenon_intro zenon_H227. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H227). zenon_intro zenon_H229. zenon_intro zenon_H228. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H228). zenon_intro zenon_H22b. zenon_intro zenon_H22a. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H22a). zenon_intro zenon_H22d. zenon_intro zenon_H22c. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H22c). zenon_intro zenon_H22f. zenon_intro zenon_H22e. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H22e). zenon_intro zenon_H4a. zenon_intro zenon_H230. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H230). zenon_intro zenon_H232. zenon_intro zenon_H231. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H231). zenon_intro zenon_H234. zenon_intro zenon_H233. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H233). zenon_intro zenon_H236. zenon_intro zenon_H235. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H235). zenon_intro zenon_H237. zenon_intro zenon_H55. % 5.74/5.92 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H16e. zenon_intro zenon_H238. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H238). zenon_intro zenon_Hf6. zenon_intro zenon_H239. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H239). zenon_intro zenon_H14f. zenon_intro zenon_H23a. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H1cb. zenon_intro zenon_H23b. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H23b). zenon_intro zenon_H169. zenon_intro zenon_H23c. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H23c). zenon_intro zenon_H1c7. zenon_intro zenon_H23d. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H23d). zenon_intro zenon_Hb7. zenon_intro zenon_H23e. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H23e). zenon_intro zenon_H10a. zenon_intro zenon_H23f. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H23f). zenon_intro zenon_H17d. zenon_intro zenon_H240. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H240). zenon_intro zenon_H140. zenon_intro zenon_H241. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H241). zenon_intro zenon_H155. zenon_intro zenon_H242. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H242). zenon_intro zenon_H1c2. zenon_intro zenon_H243. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H243). zenon_intro zenon_H105. zenon_intro zenon_H244. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H244). zenon_intro zenon_H1d1. zenon_intro zenon_H245. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H245). zenon_intro zenon_H8e. zenon_intro zenon_H246. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H246). zenon_intro zenon_Haa. zenon_intro zenon_H247. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H247). zenon_intro zenon_H18e. zenon_intro zenon_H248. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H248). zenon_intro zenon_H8f. zenon_intro zenon_H249. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H249). zenon_intro zenon_H146. zenon_intro zenon_H24a. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H24a). zenon_intro zenon_H163. zenon_intro zenon_H24b. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H24b). zenon_intro zenon_H24d. zenon_intro zenon_H24c. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H24c). zenon_intro zenon_H1e9. zenon_intro zenon_H24e. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H24e). zenon_intro zenon_H10d. zenon_intro zenon_H24f. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H24f). zenon_intro zenon_H1df. zenon_intro zenon_H250. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H250). zenon_intro zenon_H126. zenon_intro zenon_H251. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H251). zenon_intro zenon_Hf8. zenon_intro zenon_H252. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H252). zenon_intro zenon_H185. zenon_intro zenon_H253. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H253). zenon_intro zenon_H171. zenon_intro zenon_H254. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H254). zenon_intro zenon_H1e3. zenon_intro zenon_H255. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H255). zenon_intro zenon_H1bf. zenon_intro zenon_H256. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H256). zenon_intro zenon_H1e6. zenon_intro zenon_H257. % 5.74/5.92 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H191. zenon_intro zenon_H258. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H258). zenon_intro zenon_H18c. zenon_intro zenon_H259. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H259). zenon_intro zenon_H38. zenon_intro zenon_H25a. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H25a). zenon_intro zenon_H25c. zenon_intro zenon_H25b. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H25b). zenon_intro zenon_H122. zenon_intro zenon_H25d. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H25d). zenon_intro zenon_H25f. zenon_intro zenon_H25e. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H25e). zenon_intro zenon_H23. zenon_intro zenon_H260. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H260). zenon_intro zenon_H262. zenon_intro zenon_H261. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H261). zenon_intro zenon_H123. zenon_intro zenon_H263. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H263). zenon_intro zenon_H11a. zenon_intro zenon_H264. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H264). zenon_intro zenon_H1f2. zenon_intro zenon_H265. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H265). zenon_intro zenon_H202. zenon_intro zenon_H266. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H266). zenon_intro zenon_H1a6. zenon_intro zenon_H267. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H267). zenon_intro zenon_H11f. zenon_intro zenon_H268. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H268). zenon_intro zenon_H198. zenon_intro zenon_H269. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H269). zenon_intro zenon_H45. zenon_intro zenon_H26a. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H26a). zenon_intro zenon_H1ef. zenon_intro zenon_H26b. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H26b). zenon_intro zenon_H1e2. zenon_intro zenon_H26c. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H26c). zenon_intro zenon_H14b. zenon_intro zenon_H26d. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H26d). zenon_intro zenon_H174. zenon_intro zenon_H26e. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H26e). zenon_intro zenon_Hb4. zenon_intro zenon_H26f. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H26f). zenon_intro zenon_H1ff. zenon_intro zenon_H270. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H57. zenon_intro zenon_H271. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H271). zenon_intro zenon_Hce. zenon_intro zenon_H272. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H272). zenon_intro zenon_H18a. zenon_intro zenon_H273. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H273). zenon_intro zenon_H32. zenon_intro zenon_H274. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_H53. zenon_intro zenon_H275. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H72. zenon_intro zenon_H276. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H276). zenon_intro zenon_Hed. zenon_intro zenon_H277. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H277). zenon_intro zenon_H154. zenon_intro zenon_H278. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H278). zenon_intro zenon_H118. zenon_intro zenon_H279. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H279). zenon_intro zenon_H9f. zenon_intro zenon_H27a. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H27a). zenon_intro zenon_H9a. zenon_intro zenon_H27b. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H27b). zenon_intro zenon_H213. zenon_intro zenon_H27c. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H27c). zenon_intro zenon_H188. zenon_intro zenon_H27d. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H27d). zenon_intro zenon_Hdc. zenon_intro zenon_H27e. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H27e). zenon_intro zenon_H110. zenon_intro zenon_H27f. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H27f). zenon_intro zenon_H113. zenon_intro zenon_H280. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H280). zenon_intro zenon_Hf0. zenon_intro zenon_H281. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H281). zenon_intro zenon_Hd9. zenon_intro zenon_H282. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H282). zenon_intro zenon_H129. zenon_intro zenon_H283. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H283). zenon_intro zenon_H1ad. zenon_intro zenon_H284. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H284). zenon_intro zenon_H143. zenon_intro zenon_H285. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H285). zenon_intro zenon_Hf3. zenon_intro zenon_H286. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H286). zenon_intro zenon_Hfd. zenon_intro zenon_H287. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H287). zenon_intro zenon_H1a0. zenon_intro zenon_H288. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H288). zenon_intro zenon_Ha7. zenon_intro zenon_H1a3. % 5.74/5.92 apply (zenon_and_s _ _ ax4). zenon_intro zenon_Hee. zenon_intro zenon_H289. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H289). zenon_intro zenon_H63. zenon_intro zenon_H28a. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H28a). zenon_intro zenon_H6d. zenon_intro zenon_H28b. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H28b). zenon_intro zenon_H97. zenon_intro zenon_H28c. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H28c). zenon_intro zenon_H9d. zenon_intro zenon_H86. % 5.74/5.92 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H28e. zenon_intro zenon_H28d. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H28d). zenon_intro zenon_H193. zenon_intro zenon_H28f. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H28f). zenon_intro zenon_H194. zenon_intro zenon_H290. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H290). zenon_intro zenon_H189. zenon_intro zenon_H291. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H291). zenon_intro zenon_H11d. zenon_intro zenon_H292. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H292). zenon_intro zenon_H158. zenon_intro zenon_H293. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H293). zenon_intro zenon_H11e. zenon_intro zenon_H294. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H294). zenon_intro zenon_H114. zenon_intro zenon_H295. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H295). zenon_intro zenon_Hdd. zenon_intro zenon_H296. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H296). zenon_intro zenon_H115. zenon_intro zenon_H297. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H297). zenon_intro zenon_H12a. zenon_intro zenon_H298. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H298). zenon_intro zenon_H117. zenon_intro zenon_H299. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H299). zenon_intro zenon_H116. zenon_intro zenon_H29a. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H100. zenon_intro zenon_H29b. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H29b). zenon_intro zenon_H179. zenon_intro zenon_H29c. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H1a5. zenon_intro zenon_H29d. % 5.74/5.92 apply (zenon_and_s _ _ zenon_H29d). zenon_intro zenon_H195. zenon_intro zenon_Hde. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H1f | zenon_intro zenon_H29e ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H150 | zenon_intro zenon_H22 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H189); [ zenon_intro zenon_H16a | zenon_intro zenon_H33 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H3d ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.92 apply (zenon_L1_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.92 apply (zenon_L3_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.92 apply (zenon_L5_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.92 apply (zenon_L7_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.92 apply (zenon_L8_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.92 apply (zenon_L9_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.92 apply (zenon_L343_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.92 apply (zenon_L383_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.92 apply (zenon_L242_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.92 apply (zenon_L387_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.92 apply (zenon_L51_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.92 apply (zenon_L316_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.92 apply (zenon_L243_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.92 apply (zenon_L388_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.92 apply (zenon_L348_); trivial. % 5.74/5.92 apply (zenon_L284_); trivial. % 5.74/5.92 apply (zenon_L248_); trivial. % 5.74/5.92 apply (zenon_L347_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.92 apply (zenon_L1_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.92 apply (zenon_L238_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.92 apply (zenon_L313_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.92 apply (zenon_L354_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.92 apply (zenon_L8_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.92 apply (zenon_L9_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.92 apply (zenon_L343_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.92 apply (zenon_L295_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.92 apply (zenon_L242_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.92 apply (zenon_L387_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.92 apply (zenon_L51_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.92 apply (zenon_L331_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.92 apply (zenon_L299_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.92 apply (zenon_L388_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.92 apply (zenon_L303_); trivial. % 5.74/5.92 apply (zenon_L284_); trivial. % 5.74/5.92 apply (zenon_L42_); trivial. % 5.74/5.92 apply (zenon_L280_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.92 apply (zenon_L1_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.92 apply (zenon_L3_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.92 apply (zenon_L5_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.92 apply (zenon_L305_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.92 apply (zenon_L8_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.92 apply (zenon_L9_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.92 apply (zenon_L343_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.92 apply (zenon_L383_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.92 apply (zenon_L242_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.74/5.92 apply (zenon_L390_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.92 apply (zenon_L51_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.74/5.92 apply (zenon_L296_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.92 apply (zenon_L243_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.92 apply (zenon_L307_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.92 apply (zenon_L308_); trivial. % 5.74/5.92 apply (zenon_L284_); trivial. % 5.74/5.92 apply (zenon_L72_); trivial. % 5.74/5.92 apply (zenon_L278_); trivial. % 5.74/5.92 apply (zenon_L298_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.92 apply (zenon_L286_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.92 apply (zenon_L1_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.92 apply (zenon_L238_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.92 apply (zenon_L5_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.92 apply (zenon_L7_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.92 apply (zenon_L8_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.92 apply (zenon_L9_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.92 apply (zenon_L343_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.92 apply (zenon_L295_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.92 apply (zenon_L242_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.92 apply (zenon_L138_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.92 apply (zenon_L51_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.92 apply (zenon_L297_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.92 apply (zenon_L299_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.74/5.92 exact (zenon_H150 zenon_H152). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H169); [ zenon_intro zenon_H16c | zenon_intro zenon_H16b ]. % 5.74/5.92 exact (zenon_H16a zenon_H16c). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H15a | zenon_intro zenon_H16d ]. % 5.74/5.92 apply (zenon_L155_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H16d); [ zenon_intro zenon_Hb0 | zenon_intro zenon_H167 ]. % 5.74/5.92 apply (zenon_L393_); trivial. % 5.74/5.92 apply (zenon_L170_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.74/5.92 apply (zenon_L394_); trivial. % 5.74/5.92 apply (zenon_L292_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.92 apply (zenon_L303_); trivial. % 5.74/5.92 apply (zenon_L284_); trivial. % 5.74/5.92 apply (zenon_L42_); trivial. % 5.74/5.92 apply (zenon_L280_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.92 apply (zenon_L1_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.92 apply (zenon_L3_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.92 apply (zenon_L5_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.92 apply (zenon_L305_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.92 apply (zenon_L8_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.92 apply (zenon_L9_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.92 apply (zenon_L241_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.92 apply (zenon_L383_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.92 apply (zenon_L173_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.92 apply (zenon_L138_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.92 apply (zenon_L51_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.92 apply (zenon_L297_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.92 apply (zenon_L243_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.92 apply (zenon_L307_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.92 apply (zenon_L283_); trivial. % 5.74/5.92 apply (zenon_L284_); trivial. % 5.74/5.92 apply (zenon_L395_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.92 apply (zenon_L386_); trivial. % 5.74/5.92 apply (zenon_L253_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.92 apply (zenon_L1_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.92 apply (zenon_L238_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.92 apply (zenon_L5_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.92 apply (zenon_L397_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.92 apply (zenon_L8_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.92 apply (zenon_L9_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.92 apply (zenon_L343_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.92 apply (zenon_L383_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.92 apply (zenon_L242_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H152 | zenon_intro zenon_H1cc ]. % 5.74/5.92 exact (zenon_H150 zenon_H152). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H41 | zenon_intro zenon_H1cd ]. % 5.74/5.92 apply (zenon_L404_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H12b | zenon_intro zenon_H182 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.74/5.92 exact (zenon_H16a zenon_H16c). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.74/5.92 apply (zenon_L408_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.74/5.92 apply (zenon_L338_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.74/5.92 exact (zenon_Hb8 zenon_Hba). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H31 | zenon_intro zenon_H17e ]. % 5.74/5.92 apply (zenon_L19_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H28 | zenon_intro zenon_H17f ]. % 5.74/5.92 exact (zenon_H13f zenon_H28). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H74 | zenon_intro zenon_H56 ]. % 5.74/5.92 apply (zenon_L21_); trivial. % 5.74/5.92 apply (zenon_L407_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.74/5.92 apply (zenon_L409_); trivial. % 5.74/5.92 apply (zenon_L334_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H16c | zenon_intro zenon_H1c8 ]. % 5.74/5.92 exact (zenon_H16a zenon_H16c). % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1c8); [ zenon_intro zenon_H68 | zenon_intro zenon_H1c9 ]. % 5.74/5.92 apply (zenon_L408_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1c9); [ zenon_intro zenon_Hbe | zenon_intro zenon_H1c5 ]. % 5.74/5.92 apply (zenon_L417_); trivial. % 5.74/5.92 apply (zenon_L418_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.92 apply (zenon_L51_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.92 apply (zenon_L379_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.92 apply (zenon_L279_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.92 apply (zenon_L281_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.92 apply (zenon_L380_); trivial. % 5.74/5.92 apply (zenon_L284_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.92 apply (zenon_L1_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.92 apply (zenon_L3_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.92 apply (zenon_L5_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.92 apply (zenon_L305_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.92 apply (zenon_L8_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.92 apply (zenon_L9_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.92 apply (zenon_L143_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.92 apply (zenon_L383_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.92 apply (zenon_L117_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.74/5.92 apply (zenon_L390_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.92 apply (zenon_L51_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.92 apply (zenon_L379_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.92 apply (zenon_L420_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.92 apply (zenon_L307_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.92 apply (zenon_L308_); trivial. % 5.74/5.92 apply (zenon_L284_); trivial. % 5.74/5.92 apply (zenon_L72_); trivial. % 5.74/5.92 apply (zenon_L278_); trivial. % 5.74/5.92 apply (zenon_L298_); trivial. % 5.74/5.92 apply (zenon_L118_); trivial. % 5.74/5.92 apply (zenon_L60_); trivial. % 5.74/5.92 apply (zenon_L417_); trivial. % 5.74/5.92 apply (zenon_L382_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.92 apply (zenon_L342_); trivial. % 5.74/5.92 apply (zenon_L64_); trivial. % 5.74/5.92 apply (zenon_L434_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.92 apply (zenon_L1_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.92 apply (zenon_L3_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.92 apply (zenon_L313_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.92 apply (zenon_L7_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.92 apply (zenon_L8_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.92 apply (zenon_L9_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.92 apply (zenon_L106_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.92 apply (zenon_L332_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.92 apply (zenon_L242_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.74/5.92 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.74/5.92 apply (zenon_L441_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.92 apply (zenon_L51_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.92 apply (zenon_L316_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.92 apply (zenon_L243_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.92 apply (zenon_L444_); trivial. % 5.74/5.92 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.92 apply (zenon_L348_); trivial. % 5.74/5.92 apply (zenon_L284_); trivial. % 5.74/5.92 apply (zenon_L247_); trivial. % 5.74/5.92 apply (zenon_L347_); trivial. % 5.74/5.93 apply (zenon_L445_); trivial. % 5.74/5.93 apply (zenon_L337_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_L264_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L1_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L3_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L5_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L7_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L8_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L106_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L268_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L242_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L138_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L277_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L279_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L281_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L283_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L1_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L238_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L5_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L7_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L8_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L241_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L295_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L173_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L138_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L331_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L299_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.74/5.93 exact (zenon_H150 zenon_H152). % 5.74/5.93 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.74/5.93 apply (zenon_L442_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.74/5.93 apply (zenon_L394_); trivial. % 5.74/5.93 apply (zenon_L292_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L303_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L42_); trivial. % 5.74/5.93 apply (zenon_L280_); trivial. % 5.74/5.93 apply (zenon_L336_); trivial. % 5.74/5.93 apply (zenon_L448_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L1_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L3_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L5_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L7_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L8_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L106_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L332_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L242_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc0). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc1). zenon_intro zenon_H73. zenon_intro zenon_H24. % 5.74/5.93 apply (zenon_L441_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L379_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L243_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L444_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L380_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L263_); trivial. % 5.74/5.93 apply (zenon_L404_); trivial. % 5.74/5.93 apply (zenon_L389_); trivial. % 5.74/5.93 apply (zenon_L118_); trivial. % 5.74/5.93 apply (zenon_L60_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.93 apply (zenon_L411_); trivial. % 5.74/5.93 apply (zenon_L84_); trivial. % 5.74/5.93 apply (zenon_L82_); trivial. % 5.74/5.93 apply (zenon_L33_); trivial. % 5.74/5.93 apply (zenon_L38_); trivial. % 5.74/5.93 apply (zenon_L12_); trivial. % 5.74/5.93 apply (zenon_L4_); trivial. % 5.74/5.93 apply (zenon_L237_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H29e); [ zenon_intro zenon_H2c | zenon_intro zenon_H29f ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H150 | zenon_intro zenon_H22 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H189); [ zenon_intro zenon_H16a | zenon_intro zenon_H33 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H3d ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L313_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L315_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L421_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.74/5.93 apply (zenon_L464_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L472_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L474_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L348_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L216_); trivial. % 5.74/5.93 apply (zenon_L347_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L313_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L354_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L295_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L478_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.74/5.93 apply (zenon_L499_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L299_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L303_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L42_); trivial. % 5.74/5.93 apply (zenon_L280_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L501_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L305_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L421_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L502_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L426_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L474_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L307_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L308_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L72_); trivial. % 5.74/5.93 apply (zenon_L278_); trivial. % 5.74/5.93 apply (zenon_L298_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_L503_); trivial. % 5.74/5.93 apply (zenon_L213_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L147_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L487_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L421_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L173_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L277_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L279_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L281_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L283_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L147_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 5.74/5.93 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H39. zenon_intro zenon_H3e. % 5.74/5.93 apply (zenon_L504_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L295_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L478_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L138_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.74/5.93 apply (zenon_L499_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L299_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L303_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L42_); trivial. % 5.74/5.93 apply (zenon_L280_); trivial. % 5.74/5.93 apply (zenon_L506_); trivial. % 5.74/5.93 apply (zenon_L550_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L552_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L397_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L143_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L421_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L117_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L379_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L420_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.74/5.93 apply (zenon_L567_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L148_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.74/5.93 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_Hd6. zenon_intro zenon_H4c. % 5.74/5.93 apply (zenon_L569_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L487_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L421_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L117_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L379_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L279_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L281_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.74/5.93 apply (zenon_L567_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L552_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L354_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L143_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L295_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L478_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L379_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L299_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L303_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L42_); trivial. % 5.74/5.93 apply (zenon_L280_); trivial. % 5.74/5.93 apply (zenon_L570_); trivial. % 5.74/5.93 apply (zenon_L118_); trivial. % 5.74/5.93 apply (zenon_L60_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L482_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L315_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L421_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.74/5.93 apply (zenon_L464_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L472_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.93 apply (zenon_L489_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L432_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L236_); trivial. % 5.74/5.93 apply (zenon_L571_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L313_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L315_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L295_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L478_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L83_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L329_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L299_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L303_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L42_); trivial. % 5.74/5.93 apply (zenon_L280_); trivial. % 5.74/5.93 apply (zenon_L489_); trivial. % 5.74/5.93 apply (zenon_L84_); trivial. % 5.74/5.93 apply (zenon_L572_); trivial. % 5.74/5.93 apply (zenon_L82_); trivial. % 5.74/5.93 apply (zenon_L217_); trivial. % 5.74/5.93 apply (zenon_L568_); trivial. % 5.74/5.93 apply (zenon_L88_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.74/5.93 apply (zenon_L566_); trivial. % 5.74/5.93 apply (zenon_L490_); trivial. % 5.74/5.93 apply (zenon_L217_); trivial. % 5.74/5.93 apply (zenon_L568_); trivial. % 5.74/5.93 apply (zenon_L88_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H3d ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.93 apply (zenon_L98_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H152 | zenon_intro zenon_H151 ]. % 5.74/5.93 exact (zenon_H150 zenon_H152). % 5.74/5.93 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H42 | zenon_intro zenon_H153 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 5.74/5.93 exact (zenon_Hb8 zenon_Hba). % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hbb ]. % 5.74/5.93 apply (zenon_L102_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hbb); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb3 ]. % 5.74/5.93 apply (zenon_L103_); trivial. % 5.74/5.93 apply (zenon_L274_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H149 | zenon_intro zenon_H14a ]. % 5.74/5.93 apply (zenon_L480_); trivial. % 5.74/5.93 apply (zenon_L292_); trivial. % 5.74/5.93 apply (zenon_L151_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L147_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L487_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L557_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L109_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc5). zenon_intro zenon_H64. zenon_intro zenon_Hc6. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc7. zenon_intro zenon_H3e. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.74/5.93 exact (zenon_H20 zenon_H1f). % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_Hba | zenon_intro zenon_H10b ]. % 5.74/5.93 exact (zenon_Hb8 zenon_Hba). % 5.74/5.93 apply (zenon_or_s _ _ zenon_H10b); [ zenon_intro zenon_H6c | zenon_intro zenon_H10c ]. % 5.74/5.93 apply (zenon_L19_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H10c); [ zenon_intro zenon_H108 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_L494_); trivial. % 5.74/5.93 apply (zenon_L425_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.74/5.93 apply (zenon_L146_); trivial. % 5.74/5.93 apply (zenon_L486_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L279_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L281_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L283_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_L481_); trivial. % 5.74/5.93 apply (zenon_L280_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_L505_); trivial. % 5.74/5.93 apply (zenon_L298_); trivial. % 5.74/5.93 apply (zenon_L576_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_L577_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H33. zenon_intro zenon_H37. % 5.74/5.93 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_Hd6. zenon_intro zenon_H4c. % 5.74/5.93 apply (zenon_L569_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L487_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L143_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L557_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L117_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L379_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L279_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L281_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hd1). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_Hcd. zenon_intro zenon_H4c. % 5.74/5.93 apply (zenon_L562_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_L577_); trivial. % 5.74/5.93 apply (zenon_L280_); trivial. % 5.74/5.93 apply (zenon_L558_); trivial. % 5.74/5.93 apply (zenon_L118_); trivial. % 5.74/5.93 apply (zenon_L60_); trivial. % 5.74/5.93 apply (zenon_L119_); trivial. % 5.74/5.93 apply (zenon_L217_); trivial. % 5.74/5.93 apply (zenon_L568_); trivial. % 5.74/5.93 apply (zenon_L88_); trivial. % 5.74/5.93 apply (zenon_L136_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H189); [ zenon_intro zenon_H16a | zenon_intro zenon_H33 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H3d ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L31_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L449_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L421_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L456_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L578_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L579_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L348_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L95_); trivial. % 5.74/5.93 apply (zenon_L347_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L31_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L449_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L295_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L475_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L578_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L299_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L303_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L31_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L305_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L421_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hb0. zenon_intro zenon_H20. % 5.74/5.93 apply (zenon_L581_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L426_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L579_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L307_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L308_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L72_); trivial. % 5.74/5.93 apply (zenon_L278_); trivial. % 5.74/5.93 apply (zenon_L298_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L31_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L449_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L421_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L173_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L582_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L583_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L283_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L31_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L449_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L295_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L475_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L582_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L299_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L303_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L147_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L305_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L421_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L173_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L138_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L426_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hf6); [ zenon_intro zenon_H1f | zenon_intro zenon_Hf9 ]. % 5.74/5.93 exact (zenon_H20 zenon_H1f). % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hfa ]. % 5.74/5.93 apply (zenon_L458_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H39 ]. % 5.74/5.93 apply (zenon_L146_); trivial. % 5.74/5.93 apply (zenon_L304_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L307_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L308_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L72_); trivial. % 5.74/5.93 apply (zenon_L278_); trivial. % 5.74/5.93 apply (zenon_L298_); trivial. % 5.74/5.93 apply (zenon_L528_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L87_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L31_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L449_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L89_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L90_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L92_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L421_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L117_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L93_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L51_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L379_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L584_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L94_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L585_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H4c | zenon_intro zenon_H52 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H4d | zenon_intro zenon_H64 ]. % 5.74/5.93 apply (zenon_L581_); trivial. % 5.74/5.93 apply (zenon_L84_); trivial. % 5.74/5.93 apply (zenon_L528_); trivial. % 5.74/5.93 apply (zenon_L82_); trivial. % 5.74/5.93 apply (zenon_L217_); trivial. % 5.74/5.93 apply (zenon_L568_); trivial. % 5.74/5.93 apply (zenon_L530_); trivial. % 5.74/5.93 apply (zenon_L66_); trivial. % 5.74/5.93 apply (zenon_L20_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H189); [ zenon_intro zenon_H16a | zenon_intro zenon_H33 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H3d ]. % 5.74/5.93 apply (zenon_L434_); trivial. % 5.74/5.93 apply (zenon_L12_); trivial. % 5.74/5.93 apply (zenon_L4_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H29f); [ zenon_intro zenon_H52 | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H193); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H194); [ zenon_intro zenon_H150 | zenon_intro zenon_H22 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H189); [ zenon_intro zenon_H16a | zenon_intro zenon_H33 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H3d ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L3_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L590_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L600_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.74/5.93 apply (zenon_L604_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L542_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.74/5.93 apply (zenon_L607_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L222_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L532_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L590_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L544_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.74/5.93 apply (zenon_L609_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L279_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L281_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L3_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L547_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L548_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L295_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L299_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.74/5.93 apply (zenon_L607_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L42_); trivial. % 5.74/5.93 apply (zenon_L280_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L520_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L305_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L600_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L377_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L541_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L307_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L192_); trivial. % 5.74/5.93 apply (zenon_L278_); trivial. % 5.74/5.93 apply (zenon_L298_); trivial. % 5.74/5.93 apply (zenon_L60_); trivial. % 5.74/5.93 apply (zenon_L85_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L532_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L590_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L34_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Had). zenon_intro zenon_H95. zenon_intro zenon_Hae. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Haf. zenon_intro zenon_H3e. % 5.74/5.93 apply (zenon_L604_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.74/5.93 apply (zenon_L618_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L346_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L222_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L76_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L590_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L34_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L208_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L619_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L279_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L281_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L532_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L547_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L548_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L295_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L299_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L346_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L280_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L532_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L621_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L39_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L306_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.74/5.93 apply (zenon_L623_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Ha6. zenon_intro zenon_Hcc. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_H89. zenon_intro zenon_H24. % 5.74/5.93 apply (zenon_L625_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L222_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L532_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L621_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L39_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L306_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L50_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L279_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L281_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L520_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L305_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L39_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L306_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L50_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.74/5.93 apply (zenon_L623_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L307_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L278_); trivial. % 5.74/5.93 apply (zenon_L85_); trivial. % 5.74/5.93 apply (zenon_L64_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_L572_); trivial. % 5.74/5.93 apply (zenon_L217_); trivial. % 5.74/5.93 apply (zenon_L568_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.74/5.93 apply (zenon_L599_); trivial. % 5.74/5.93 apply (zenon_L85_); trivial. % 5.74/5.93 apply (zenon_L33_); trivial. % 5.74/5.93 apply (zenon_L38_); trivial. % 5.74/5.93 apply (zenon_L88_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L532_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L616_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L200_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L626_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L484_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L606_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L228_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L3_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L616_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L544_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L626_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L279_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L281_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L520_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L305_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L200_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L377_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L484_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L307_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L278_); trivial. % 5.74/5.93 apply (zenon_L617_); trivial. % 5.74/5.93 apply (zenon_L620_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_L565_); trivial. % 5.74/5.93 apply (zenon_L217_); trivial. % 5.74/5.93 apply (zenon_L568_); trivial. % 5.74/5.93 apply (zenon_L627_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H11d); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H3d ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H11e); [ zenon_intro zenon_H24 | zenon_intro zenon_H2c ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H115); [ zenon_intro zenon_H4b | zenon_intro zenon_Hbe ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hca ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_L596_); trivial. % 5.74/5.93 apply (zenon_L139_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L3_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L573_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L544_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L557_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L279_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L281_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L629_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L532_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L305_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L611_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L377_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L109_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L615_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L307_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L139_); trivial. % 5.74/5.93 apply (zenon_L278_); trivial. % 5.74/5.93 apply (zenon_L298_); trivial. % 5.74/5.93 apply (zenon_L60_); trivial. % 5.74/5.93 apply (zenon_L85_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H58 | zenon_intro zenon_Ha6 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H59 | zenon_intro zenon_Hd3 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H195); [ zenon_intro zenon_H3e | zenon_intro zenon_H60 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L532_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L573_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L34_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L630_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L615_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L595_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L263_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L76_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L573_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L34_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L208_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L630_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L109_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_L279_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L281_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L629_); trivial. % 5.74/5.93 apply (zenon_L60_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H1d | zenon_intro zenon_Hdf ]. % 5.74/5.93 apply (zenon_L16_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_H2f | zenon_intro zenon_He0 ]. % 5.74/5.93 apply (zenon_L532_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_H36 | zenon_intro zenon_He1 ]. % 5.74/5.93 apply (zenon_L58_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_H3b | zenon_intro zenon_He2 ]. % 5.74/5.93 apply (zenon_L573_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_H3f | zenon_intro zenon_He3 ]. % 5.74/5.93 apply (zenon_L39_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He3); [ zenon_intro zenon_H43 | zenon_intro zenon_He4 ]. % 5.74/5.93 apply (zenon_L9_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hd7 | zenon_intro zenon_He5 ]. % 5.74/5.93 apply (zenon_L59_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Had | zenon_intro zenon_He6 ]. % 5.74/5.93 apply (zenon_L306_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hbc | zenon_intro zenon_He7 ]. % 5.74/5.93 apply (zenon_L190_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Hc0 | zenon_intro zenon_He8 ]. % 5.74/5.93 apply (zenon_L61_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc3 | zenon_intro zenon_He9 ]. % 5.74/5.93 apply (zenon_L62_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hea ]. % 5.74/5.93 apply (zenon_L310_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Heb ]. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9. % 5.74/5.93 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_Hb3. zenon_intro zenon_H20. % 5.74/5.93 apply (zenon_L622_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hec ]. % 5.74/5.93 apply (zenon_L595_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hd4 ]. % 5.74/5.93 apply (zenon_L63_); trivial. % 5.74/5.93 apply (zenon_L284_); trivial. % 5.74/5.93 apply (zenon_L64_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H26 | zenon_intro zenon_H95 ]. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H77 | zenon_intro zenon_Hc2 ]. % 5.74/5.93 apply (zenon_L576_); trivial. % 5.74/5.93 apply (zenon_L60_); trivial. % 5.74/5.93 apply (zenon_L217_); trivial. % 5.74/5.93 apply (zenon_L568_); trivial. % 5.74/5.93 apply (zenon_L631_); trivial. % 5.74/5.93 apply (zenon_L136_); trivial. % 5.74/5.93 apply (zenon_L531_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H13f | zenon_intro zenon_H41 ]. % 5.74/5.93 apply (zenon_L429_); trivial. % 5.74/5.93 apply (zenon_or_s _ _ zenon_H114); [ zenon_intro zenon_H25 | zenon_intro zenon_H46 ]. % 5.74/5.93 apply (zenon_L448_); trivial. % 5.74/5.93 apply (zenon_L38_); trivial. % 5.74/5.93 apply (zenon_L263_); trivial. % 5.74/5.93 Qed. % 5.74/5.93 % SZS output end Proof % 5.74/5.93 (* END-PROOF *) % 5.74/5.93 nodes searched: 165635 % 5.74/5.93 max branch formulas: 316 % 5.74/5.93 proof nodes created: 7140 % 5.74/5.93 formulas created: 49001 % 5.74/5.93 %------------------------------------------------------------------------------